{
 "cells": [
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   "source": [
    "<div style=\"text-align: right\">Peter Norvig, 12 Feb 2016<br>Revised 17 Feb 2018</div> \n",
    "\n",
    "# A Concrete Introduction to Probability (using Python)\n",
    "\n",
    "In 1814, Pierre-Simon Laplace [wrote](https://en.wikipedia.org/wiki/Classical_definition_of_probability):\n",
    "\n",
    ">*Probability theory is nothing but common sense reduced to calculation. ... [Probability] is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible ... when nothing leads us to expect that any one of these cases should occur more than any other.*\n",
    "\n",
    "![Laplace](https://upload.wikimedia.org/wikipedia/commons/thumb/3/30/AduC_197_Laplace_%28P.S.%2C_marquis_de%2C_1749-1827%29.JPG/180px-AduC_197_Laplace_%28P.S.%2C_marquis_de%2C_1749-1827%29.JPG)\n",
    "<center><a href=\"https://en.wikipedia.org/wiki/Pierre-Simon_Laplace\">Pierre-Simon Laplace</a><br>1814</center>\n",
    "\n",
    "\n",
    "Laplace nailed it. To untangle a probability problem, all you have to do is define exactly what the cases are, and careful count the favorable and total cases. Let's be clear on our vocabulary words:\n",
    "\n",
    "\n",
    "- **[Trial](https://en.wikipedia.org/wiki/Experiment_(probability_theory%29):**\n",
    "  A single occurrence with an outcome that is uncertain until we observe it. \n",
    "  <br>*For example, rolling a single die.*\n",
    "- **[Outcome](https://en.wikipedia.org/wiki/Outcome_(probability%29):**\n",
    "  A possible result of a trial; one particular state of the world. What Laplace calls a **case.**\n",
    "  <br>*For example:* `4`.\n",
    "- **[Sample Space](https://en.wikipedia.org/wiki/Sample_space):**\n",
    "  The set of all possible outcomes for the trial. \n",
    "  <br>*For example,* `{1, 2, 3, 4, 5, 6}`.\n",
    "- **[Event](https://en.wikipedia.org/wiki/Event_(probability_theory%29):**\n",
    "  A subset of outcomes that together have some property we are interested in.\n",
    "  <br>*For example, the event \"even die roll\" is the set of outcomes* `{2, 4, 6}`. \n",
    "- **[Probability](https://en.wikipedia.org/wiki/Probability_theory):**\n",
    "  As Laplace said, the probability of an event with respect to a sample space is the \"number of favorable cases\" (outcomes from the sample space that are in the event) divided by the \"number of all the cases\" in the sample space (assuming \"nothing leads us to expect that any one of these cases should occur more than any other\"). Since this is a proper fraction, probability will always be a number between 0 (representing an impossible event) and 1 (representing a certain event).\n",
    "<br>*For example, the probability of an even die roll is 3/6 = 1/2.*\n",
    "\n",
    "This notebook will explore these concepts in a concrete way using Python code. The code is meant to be succint and explicit, and fast enough to handle sample spaces with millions of outcomes. If you need to handle trillions, you'll want a more efficient implementation. I also have  [another notebook](http://nbviewer.jupyter.org/url/norvig.com/ipython/ProbabilityParadox.ipynb) that covers  paradoxes in Probability Theory. "
   ]
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   "source": [
    "# `P` is for Probability\n",
    "\n",
    "The code below implements Laplace's quote directly: *Probability is thus simply a fraction whose numerator is the number of favorable cases and whose denominator is the number of all the cases possible.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
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   "outputs": [],
   "source": [
    "from fractions import Fraction\n",
    "\n",
    "def P(event, space): \n",
    "    \"The probability of an event, given a sample space.\"\n",
    "    return Fraction(cases(favorable(event, space)), \n",
    "                    cases(space))\n",
    "\n",
    "favorable = set.intersection # Outcomes that are in the event and in the sample space\n",
    "cases     = len              # The number of cases is the length, or size, of a set"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    " \n",
    "# Warm-up Problem: Die Roll"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "What's the probability of rolling an even number with a single six-sided fair die? Mathematicians traditionally use a single capital letter to denote a sample space; I'll use `D` for the die:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
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    "deletable": true,
    "new_sheet": false,
    "run_control": {
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(1, 2)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D     = {1, 2, 3, 4, 5, 6} # a sample space\n",
    "even  = {   2,    4,    6} # an event\n",
    "\n",
    "P(even, D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Good to confirm what we already knew. We can explore some other events:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "prime = {2, 3, 5, 7, 11, 13}\n",
    "odd   = {1, 3, 5, 7, 9, 11, 13}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(1, 2)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(odd, D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(5, 6)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P((even | prime), D) # The probability of an even or prime die roll"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(1, 3)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P((odd & prime), D) # The probability of an odd prime die roll"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
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   },
   "source": [
    "# Card Problems\n",
    "\n",
    "Consider dealing a hand of five playing cards. An individual card has a rank and  suit, like `'J♥'` for the Jack of Hearts, and a `deck` has 52 cards:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "52"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suits = u'♥♠♦♣'\n",
    "ranks = u'AKQJT98765432'\n",
    "deck  = [r + s for r in ranks for s in suits]\n",
    "len(deck)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now I want to define `Hands` as the sample space of all 5-card combinations from `deck`. The function `itertools.combinations` does most of the work; we than concatenate each combination into a space-separated string:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "2598960"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import itertools\n",
    "\n",
    "def combos(items, n):\n",
    "    \"All combinations of n items; each combo as a space-separated str.\"\n",
    "    return set(map(' '.join, itertools.combinations(items, n)))\n",
    "\n",
    "Hands = combos(deck, 5)\n",
    "len(Hands)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are too many hands to look at them all, but we can sample:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Q♥ J♥ J♠ J♦ 6♠',\n",
       " 'J♥ T♠ 9♥ 8♦ 3♣',\n",
       " 'T♣ 8♣ 6♥ 5♠ 4♠',\n",
       " 'A♦ 8♠ 7♥ 7♠ 2♣',\n",
       " 'A♥ J♠ J♦ 9♠ 9♦',\n",
       " 'K♠ 8♠ 8♦ 7♦ 5♦',\n",
       " 'J♥ J♣ T♥ 5♠ 4♥']"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "random.sample(Hands, 7)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['6♥', '5♦', 'Q♠', 'A♥', '9♣', '3♠', '8♥']"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "random.sample(deck, 7)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Now we can answer questions like the probability of being dealt a flush (5 cards of the same suit):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(33, 16660)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flush = {hand for hand in Hands if any(hand.count(suit) == 5 for suit in suits)}\n",
    "\n",
    "P(flush, Hands)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "Or the probability of four of a kind:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "button": false,
    "collapsed": false,
    "new_sheet": false,
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(1, 4165)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "four_kind = {hand for hand in Hands if any(hand.count(rank) == 4 for rank in ranks)}\n",
    "\n",
    "P(four_kind, Hands)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
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   },
   "source": [
    "\n",
    "\n",
    "# Urn Problems\n",
    "\n",
    "Around 1700, Jacob Bernoulli wrote about removing colored balls from an urn in his landmark treatise *[Ars Conjectandi](https://en.wikipedia.org/wiki/Ars_Conjectandi)*, and ever since then, explanations of probability have relied on [urn problems](https://www.google.com/search?q=probability+ball+urn). (You'd think the urns would be empty by now.) \n",
    "\n",
    "![Jacob Bernoulli](http://www2.stetson.edu/~efriedma/periodictable/jpg/Bernoulli-Jacob.jpg)\n",
    "<center><a href=\"https://en.wikipedia.org/wiki/Jacob_Bernoulli\">Jacob Bernoulli</a><br>1700</center>\n",
    "\n",
    "For example, here is a three-part problem [adapted](http://mathforum.org/library/drmath/view/69151.html)  from mathforum.org:\n",
    "\n",
    "> *An urn contains 6 blue, 9 red, and 8 white balls.  We select six balls at random. What is the probability of each of these  outcomes:*\n",
    "\n",
    "> - *All balls are red*.\n",
    "- *3 are blue, and 1 is red, and 2 are white, *.\n",
    "- *Exactly 4 balls are white*.\n",
    "\n",
    "We'll start by defining the contents of the urn. A `set` can't contain multiple objects that are equal to each other, so I'll call the blue balls `'B1'` through `'B6'`, rather than trying to have 6 balls all called `'B'`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'B1',\n",
       " 'B2',\n",
       " 'B3',\n",
       " 'B4',\n",
       " 'B5',\n",
       " 'B6',\n",
       " 'R1',\n",
       " 'R2',\n",
       " 'R3',\n",
       " 'R4',\n",
       " 'R5',\n",
       " 'R6',\n",
       " 'R7',\n",
       " 'R8',\n",
       " 'R9',\n",
       " 'W1',\n",
       " 'W2',\n",
       " 'W3',\n",
       " 'W4',\n",
       " 'W5',\n",
       " 'W6',\n",
       " 'W7',\n",
       " 'W8'}"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def balls(color, n):\n",
    "    \"A set of n numbered balls of the given color.\"\n",
    "    return {color + str(i)\n",
    "            for i in range(1, n + 1)}\n",
    "\n",
    "urn = balls('B', 6) | balls('R', 9) | balls('W', 8)\n",
    "urn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   },
   "source": [
    "Now we can define the sample space, `U6`, as the set of all 6-ball combinations:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "['W1 R4 W3 R7 R2 W7',\n",
       " 'R3 W1 B6 W3 R2 W7',\n",
       " 'R3 W5 B4 B2 W8 W7',\n",
       " 'W2 B1 R3 B2 R8 B5',\n",
       " 'B1 R5 W6 R9 R7 B5']"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "U6 = combos(urn, 6)\n",
    "\n",
    "random.sample(U6, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define  `select` such that `select('R', 6)` is the event of picking 6 red balls from the urn:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def select(color, n, space=U6):\n",
    "    \"The subset of the sample space with exactly `n` balls of given `color`.\"\n",
    "    return {s for s in space if s.count(color) == n}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now I can answer the three questions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(4, 4807)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(select('R', 6), U6) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(240, 4807)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(select('B', 3)  & select('R', 1) & select('W', 2), U6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Fraction(350, 4807)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(select('W', 4), U6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
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   },
   "source": [
    "## Urn problems via arithmetic\n",
    "\n",
    "Let's verify these calculations using basic arithmetic, rather than exhaustive counting. First, how many ways can I choose 6 out of 9 red balls? It could be any of the 9 for the first ball, any of 8 remaining for the second, and  so on down to any of the remaining 4 for the sixth and final ball. But we don't care about the *order* of the six balls, so divide that product by the number of permutations of 6 things, which is 6!, giving us \n",
    "9 &times; 8 &times; 7 &times; 6 &times; 5 &times; 4 / 6! = 84. In general, the number of ways of choosing *c* out of *n* items is (*n* choose *c*) = *n*! / ((*n* - *c*)! &times; c!).\n",
    "We can translate that to code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
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    "collapsed": true,
    "deletable": true,
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   },
   "outputs": [],
   "source": [
    "from math import factorial\n",
    "\n",
    "def choose(n, c):\n",
    "    \"Number of ways to choose c items from a list of n items.\"\n",
    "    return factorial(n) // (factorial(n - c) * factorial(c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "84"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "choose(9, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can verify the answers to the three problems. (Since `P` computes a ratio and `choose` computes a count,\n",
    "I multiply the left-hand-side by `N`, the length of the sample space, to make both sides be counts.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = len(U6)\n",
    "\n",
    "N * P(select('R', 6), U6) == choose(9, 6)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N * P(select('B', 3) & select('W', 2) & select('R', 1), U6) == choose(6, 3) * choose(8, 2) * choose(9, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N * P(select('W', 4), U6) == choose(8, 4) * choose(6 + 9, 2)  # (6 + 9 non-white balls)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can solve all these problems just by counting; all you ever needed to know about probability problems you learned from Sesame Street:\n",
    "\n",
    "![The Count](http://img2.oncoloring.com/count-dracula-number-thir_518b77b54ba6c-p.gif)\n",
    "<center><a href=\"https://en.wikipedia.org/wiki/Count_von_Count\">The Count</a><br>1972&mdash;</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "# Non-Equiprobable Outcomes\n",
    "\n",
    "So far, we have accepted Laplace's assumption that *nothing leads us to expect that any one of these cases should occur more than any other*.\n",
    "In real life, we often get outcomes that are not equiprobable--for example, a loaded die favors one side over the others.  We will introduce three more vocabulary items:\n",
    "\n",
    "* [Frequency](https://en.wikipedia.org/wiki/Frequency_%28statistics%29): a non-negative number describing how often an outcome occurs. Can be a count like 5, or a ratio like 1/6.\n",
    "\n",
    "* [Distribution](http://mathworld.wolfram.com/StatisticalDistribution.html): A mapping from outcome to frequency of that outcome. We will allow sample spaces to be distributions. \n",
    "\n",
    "* [Probability Distribution](https://en.wikipedia.org/wiki/Probability_distribution): A probability distribution\n",
    "is a distribution whose frequencies sum to 1. \n",
    "\n",
    "\n",
    "I could implement distributions with `Dist = dict`, but instead I'll make `Dist` a subclass `collections.Counter`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "        \n",
    "class Dist(Counter): \n",
    "    \"A Distribution of {outcome: frequency} pairs.\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because a `Dist` is a `Counter`, we can initialize it in any of the following ways:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dist({1: 1, 2: 1, 3: 1, 4: 1, 5: 1, 6: 1})"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A set of equiprobable outcomes:\n",
    "Dist({1, 2, 3, 4, 5, 6})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dist({'H': 5, 'T': 4})"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A collection of outcomes, with repetition indicating frequency:\n",
    "Dist('THHHTTHHT')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dist({'H': 5, 'T': 4})"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A mapping of {outcome: frequency} pairs:\n",
    "Dist({'H': 5, 'T': 4})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Keyword arguments:\n",
    "Dist(H=5, T=4) == Dist({'H': 5}, T=4) == Dist('TTTT', H=5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now I will modify the code to handle distributions.\n",
    "Here's my plan:\n",
    "\n",
    "- Sample spaces and events can both be specified as either a `set` or a `Dist`.\n",
    "- The sample space can be a non-probability distribution like `Dist(H=50, T=50)`; the results\n",
    "will be the same as if the sample space had been a true probability distribution like `Dist(H=1/2, T=1/2)`.\n",
    "- The function `cases` now sums the frequencies in a distribution (it previously counted the length).\n",
    "- The function `favorable` now returns a `Dist` of favorable outcomes and their frequencies (not a `set`).\n",
    "- I will redefine `Fraction` to use `\"/\"`, not `fractions.Fraction`, because frequencies might be floats.\n",
    "- `P` is unchanged.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def cases(outcomes): \n",
    "    \"The total frequency of all the outcomes.\"\n",
    "    return sum(Dist(outcomes).values())\n",
    "\n",
    "def favorable(event, space):\n",
    "    \"A distribution of outcomes from the sample space that are in the event.\"\n",
    "    space = Dist(space)\n",
    "    return Dist({x: space[x] \n",
    "                 for x in space if x in event})\n",
    "\n",
    "def Fraction(n, d): return n / d"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, here's the probability of rolling an even number with a crooked die that is loaded to prefer 6:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Crooked = Dist({1: 0.1, 2: 0.1, 3: 0.1, 4: 0.1, 5: 0.1, 6: 0.5})\n",
    "\n",
    "P(even, Crooked)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As another example, an [article](http://people.kzoo.edu/barth/math105/moreboys.pdf) gives the following counts for two-child families in Denmark, where `GB` means a family where the first child is a girl and the second a boy (I'm aware that not all births can be classified as the binary \"boy\" or \"girl,\" but the data was reported that way):\n",
    "\n",
    "    GG: 121801    GB: 126840\n",
    "    BG: 127123    BB: 135138"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "button": false,
    "collapsed": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "DK = Dist(GG=121801, GB=126840,\n",
    "          BG=127123, BB=135138)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48667063350701306"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_girl  = {'GG', 'GB'}\n",
    "P(first_girl, DK)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4872245557856497"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "second_girl = {'GG', 'BG'}\n",
    "P(second_girl, DK)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "This says that the probability of a girl is somewhere between 48% and 49%. The probability of a girl is very slightly higher for the second child. \n",
    "\n",
    "Given the first child, are you more likely to have a second child of the same sex?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5029124959385557"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "same = {'GG', 'BB'}\n",
    "P(same, DK)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Yes, but only by about 0.3%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "# Predicates as events\n",
    "\n",
    "To calculate the probability of an even die roll, I originally said\n",
    "\n",
    "    even = {2, 4, 6}\n",
    "    \n",
    "But that's inelegant&mdash;I had to explicitly enumerate all the even numbers from one to six. If I ever wanted to deal with a twelve or twenty-sided die, I would have to go back and redefine `even`.  I would prefer to define `even` once and for all like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "button": false,
    "collapsed": true,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "def even(n): return n % 2 == 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Now in order to make `P(even, D)` work, I'll allow an `Event` to be either a collection of outcomes or a `callable` predicate (that is, a function that returns true for outcomes that are part of the event). I don't need to modify `P`, but  `favorable` will have  to convert a callable `event` to a `set`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "button": false,
    "collapsed": true,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "def favorable(event, space):\n",
    "    \"A distribution of outcomes from the sample space that are in the event.\"\n",
    "    if callable(event):\n",
    "        event = {x for x in space if event(x)}\n",
    "    space = Dist(space)\n",
    "    return Dist({x: space[x] \n",
    "                 for x in space if x in event})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dist({2: 1, 4: 1, 6: 1})"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "favorable(even, D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(even, D)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'll define `die` to make a sample space for an *n*-sided die:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def die(n): return set(range(1, n + 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dist({2: 1, 4: 1, 6: 1, 8: 1, 10: 1, 12: 1})"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "favorable(even, die(12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(even, die(12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(even, die(2000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.49975012493753124"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(even, die(2001))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "We can define more interesting events using predicates; for example we can determine the probability that the sum of  rolling *d* 6-sided dice is prime:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "P(is_prime, sum_dice(1)) = 0.5\n",
      "P(is_prime, sum_dice(2)) = 0.417\n",
      "P(is_prime, sum_dice(3)) = 0.338\n",
      "P(is_prime, sum_dice(4)) = 0.333\n",
      "P(is_prime, sum_dice(5)) = 0.317\n",
      "P(is_prime, sum_dice(6)) = 0.272\n",
      "P(is_prime, sum_dice(7)) = 0.242\n",
      "P(is_prime, sum_dice(8)) = 0.236\n"
     ]
    }
   ],
   "source": [
    "def sum_dice(d): return Dist(sum(dice) for dice in itertools.product(D, repeat=d))\n",
    "\n",
    "def is_prime(n): return (n > 1 and not any(n % i == 0 for i in range(2, n)))\n",
    "\n",
    "for d in range(1, 9):\n",
    "    p = P(is_prime, sum_dice(d))\n",
    "    print(\"P(is_prime, sum_dice({})) = {}\".format(d, round(p, 3)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fermat and Pascal: The Unfinished Game\n",
    "\n",
    "<table>\n",
    "<tr><td><img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/9/98/Pierre_de_Fermat2.png/140px-Pierre_de_Fermat2.png\"><center><a href=\"https://en.wikipedia.org/wiki/Pierre_de_Fermat\">Pierre de Fermat</a><br>1654\n",
    "<td><img src=\"https://www.umass.edu/wsp/images/pascal.jpg\"><center><a href=\"https://en.wikipedia.org/wiki/Blaise_Pascal\">Blaise Pascal]</a><br>1654\n",
    "</table>\n",
    "\n",
    "Consider a gambling game consisting of tossing a coin repeatedly. Player H wins the game as soon as a total of 10 heads come up, and T wins if a total of 10 tails come up before H wins. If the game is interrupted when H has 8 heads and T has 7 tails, how should the pot of money (which happens to be 100 Francs) be split?  Here are some proposals, and arguments against them:\n",
    "- It is uncertain, so just split the pot 50-50. \n",
    "<br>*No, because surely H is more likely to win.*\n",
    "- In proportion to each player's current score, so H gets a 8/(8+7) share. \n",
    "<br>*No, because if the score was 0 heads to 1 tail, H should get more than 0/1.*\n",
    "- In proportion to how many tosses the opponent needs to win, so H gets 3/(3+2). \n",
    "<br>*This seems better, but no, if H is 9 away and T is only 1 away from winning, then it seems that giving H a 1/10 share is too much.*\n",
    "\n",
    "In 1654, Blaise Pascal and Pierre de Fermat corresponded on this problem, with Fermat [writing](http://mathforum.org/isaac/problems/prob1.html):\n",
    "\n",
    ">Dearest Blaise,\n",
    "\n",
    ">As to the problem of how to divide the 100 Francs, I think I have found a solution that you will find to be fair. Seeing as I needed only two points to win the game, and you needed 3, I think we can establish that after four more tosses of the coin, the game would have been over. For, in those four tosses, if you did not get the necessary 3 points for your victory, this would imply that I had in fact gained the necessary 2 points for my victory. In a similar manner, if I had not achieved the necessary 2 points for my victory, this would imply that you had in fact achieved at least 3 points and had therefore won the game. Thus, I believe the following list of possible endings to the game is exhaustive. I have denoted 'heads' by an 'h', and tails by a 't.' I have starred the outcomes that indicate a win for myself.\n",
    "\n",
    ">       h h h h *       h h h t *       h h t h *       h h t t *\n",
    ">       h t h h *       h t h t *       h t t h *       h t t t\n",
    ">       t h h h *       t h h t *       t h t h *       t h t t\n",
    ">       t t h h *       t t h t         t t t h         t t t t\n",
    "\n",
    ">I think you will agree that all of these outcomes are equally likely. Thus I believe that we should divide the stakes by the ration 11:5 in my favor, that is, I should receive (11/16)&times;100 = 68.75 Francs, while you should receive 31.25 Francs.\n",
    "\n",
    "\n",
    ">I hope all is well in Paris,\n",
    "\n",
    ">Your friend and colleague,\n",
    "\n",
    ">Pierre\n",
    "\n",
    "Pascal agreed with this solution, and [replied](http://mathforum.org/isaac/problems/prob2.html) with a generalization that made use of his previous invention, Pascal's Triangle. There's even [a book](https://smile.amazon.com/Unfinished-Game-Pascal-Fermat-Seventeenth-Century/dp/0465018963?sa-no-redirect=1) about it.\n",
    "\n",
    "We can solve the problem with the tools we have:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def win_unfinished_game(h, t):\n",
    "    \"The probability that H will win the unfinished game, given the number of points needed by H and T to win.\"\n",
    "    return P(at_least(h, 'h'), finishes(h, t))\n",
    "\n",
    "def at_least(n, item):\n",
    "    \"The event of getting at least n instances of item in an outcome.\"\n",
    "    return lambda outcome: outcome.count(item) >= n\n",
    "    \n",
    "def finishes(h, t):\n",
    "    \"All finishes of a game where player H needs h points to win and T needs t.\"\n",
    "    tosses = ['ht'] * (h + t - 1)\n",
    "    return set(itertools.product(*tosses))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can generate the 16 equiprobable finished that Pierre wrote about:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{('h', 'h', 'h', 'h'),\n",
       " ('h', 'h', 'h', 't'),\n",
       " ('h', 'h', 't', 'h'),\n",
       " ('h', 'h', 't', 't'),\n",
       " ('h', 't', 'h', 'h'),\n",
       " ('h', 't', 'h', 't'),\n",
       " ('h', 't', 't', 'h'),\n",
       " ('h', 't', 't', 't'),\n",
       " ('t', 'h', 'h', 'h'),\n",
       " ('t', 'h', 'h', 't'),\n",
       " ('t', 'h', 't', 'h'),\n",
       " ('t', 'h', 't', 't'),\n",
       " ('t', 't', 'h', 'h'),\n",
       " ('t', 't', 'h', 't'),\n",
       " ('t', 't', 't', 'h'),\n",
       " ('t', 't', 't', 't')}"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "finishes(2, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can find the 11 of them that are favorable to player `H`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dist({('h', 'h', 'h', 'h'): 1,\n",
       "      ('h', 'h', 'h', 't'): 1,\n",
       "      ('h', 'h', 't', 'h'): 1,\n",
       "      ('h', 'h', 't', 't'): 1,\n",
       "      ('h', 't', 'h', 'h'): 1,\n",
       "      ('h', 't', 'h', 't'): 1,\n",
       "      ('h', 't', 't', 'h'): 1,\n",
       "      ('t', 'h', 'h', 'h'): 1,\n",
       "      ('t', 'h', 'h', 't'): 1,\n",
       "      ('t', 'h', 't', 'h'): 1,\n",
       "      ('t', 't', 'h', 'h'): 1})"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "favorable(at_least(2, 'h'), finishes(2, 3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Finally, we can answer the question:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "68.75"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "100 * win_unfinished_game(2, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We agree with Pascal and Fermat; we're in good company!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Newton's Answer to a Problem by Pepys\n",
    "\n",
    "<table>\n",
    "<tr><td><img src=\"http://scienceworld.wolfram.com/biography/pics/Newton.jpg\"><center><a href=\"https://en.wikipedia.org/wiki/Isaac_Newton\">Isaac Newton</a><br>1693</center>\n",
    "<td><img src=\"https://upload.wikimedia.org/wikipedia/commons/thumb/f/f8/Samuel_Pepys_portrait.jpg/148px-Samuel_Pepys_portrait.jpg\"><center><a href=\"https://en.wikipedia.org/wiki/Samuel_Pepys\">Samuel Pepys</a><br>1693</center>\n",
    "</table>\n",
    "\n",
    "Let's jump ahead from 1654 all the way to 1693, [when](http://fermatslibrary.com/s/isaac-newton-as-a-probabilist) Samuel Pepys wrote to Isaac Newton posing the problem:\n",
    "\n",
    "> Which of the following three propositions has the greatest chance of success? \n",
    "  1. Six fair dice are tossed independently and at least one “6” appears. \n",
    "  2. Twelve fair dice are tossed independently and at least two “6”s appear. \n",
    "  3. Eighteen fair dice are tossed independently and at least three “6”s appear.\n",
    "  \n",
    "Newton was able to answer the question correctly (although his reasoning was not quite right); let's see how we can do. Since we're only interested in whether a die comes up as \"6\" or not, we can define a single die like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "die6 = Dist({6: 1/6, '-': 5/6})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we can define the joint distribution formed by combining two independent distribution like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dist({'--': 0.6944444444444445,\n",
       "      '-6': 0.1388888888888889,\n",
       "      '6-': 0.1388888888888889,\n",
       "      '66': 0.027777777777777776})"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def joint(A, B, combine='{}{}'.format):\n",
    "    \"\"\"The joint distribution of two independent distributions. \n",
    "    Result is all entries of the form {'ab': frequency(a) * frequency(b)}\"\"\"\n",
    "    return Dist({combine(a, b): A[a] * B[b]\n",
    "                 for a in A for b in B})\n",
    "\n",
    "joint(die6, die6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "And the joint distribution from rolling *n* dice:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dist({'----': 0.48225308641975323,\n",
       "      '---6': 0.09645061728395063,\n",
       "      '--6-': 0.09645061728395063,\n",
       "      '--66': 0.019290123456790122,\n",
       "      '-6--': 0.09645061728395063,\n",
       "      '-6-6': 0.019290123456790122,\n",
       "      '-66-': 0.019290123456790122,\n",
       "      '-666': 0.0038580246913580245,\n",
       "      '6---': 0.09645061728395063,\n",
       "      '6--6': 0.019290123456790126,\n",
       "      '6-6-': 0.019290123456790126,\n",
       "      '6-66': 0.0038580246913580245,\n",
       "      '66--': 0.019290123456790126,\n",
       "      '66-6': 0.0038580246913580245,\n",
       "      '666-': 0.0038580246913580245,\n",
       "      '6666': 0.0007716049382716049})"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def dice(n, die):\n",
    "    \"Joint probability distribution from rolling `n` dice.\"\n",
    "    if n == 1:\n",
    "        return die\n",
    "    else:\n",
    "        return joint(die, dice(n - 1, die))\n",
    "    \n",
    "dice(4, die6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are ready to determine which proposition is more likely to have the required number of sixes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.665102023319616"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(at_least(1, '6'), dice(6, die6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.61866737373231"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(at_least(2, '6'), dice(12, die6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5973456859477678"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P(at_least(3, '6'), dice(18, die6))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We reach the same conclusion Newton did, that the best chance is rolling six dice."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "# More Urn Problems: M&Ms and Bayes\n",
    "\n",
    "Here's another urn problem (actually a \"bag\" problem) [from](http://allendowney.blogspot.com/2011/10/my-favorite-bayess-theorem-problems.html) prolific Python/Probability pundit [Allen Downey ](http://allendowney.blogspot.com/):\n",
    "\n",
    "> The blue M&M was introduced in 1995.  Before then, the color mix in a bag of plain M&Ms was (30% Brown, 20% Yellow, 20% Red, 10% Green, 10% Orange, 10% Tan).  Afterward it was (24% Blue , 20% Green, 16% Orange, 14% Yellow, 13% Red, 13% Brown). \n",
    "A friend of mine has two bags of M&Ms, and he tells me that one is from 1994 and one from 1996.  He won't tell me which is which, but he gives me one M&M from each bag.  One is yellow and one is green.  What is the probability that the yellow M&M came from the 1994 bag?\n",
    "\n",
    "To solve this problem, we'll first create distributions for each bag: `bag94` and `bag96`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "button": false,
    "collapsed": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "bag94 = Dist(brown=30, yellow=20, red=20, green=10, orange=10, tan=10)\n",
    "bag96 = Dist(blue=24, green=20, orange=16, yellow=14, red=13, brown=13)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "Next, define `MM` as the joint distribution&mdash;the sample space for picking one M&M from each bag. The outcome `'94:yellow 96:green'` means that a yellow M&M was selected from the 1994 bag and a green one from the 1996 bag. In this problem we don't get to see the actual outcome; we just see some evidence about the outcome, that it contains a yellow and a green."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "button": false,
    "collapsed": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dist({'94:brown 96:blue': 720,\n",
       "      '94:brown 96:brown': 390,\n",
       "      '94:brown 96:green': 600,\n",
       "      '94:brown 96:orange': 480,\n",
       "      '94:brown 96:red': 390,\n",
       "      '94:brown 96:yellow': 420,\n",
       "      '94:green 96:blue': 240,\n",
       "      '94:green 96:brown': 130,\n",
       "      '94:green 96:green': 200,\n",
       "      '94:green 96:orange': 160,\n",
       "      '94:green 96:red': 130,\n",
       "      '94:green 96:yellow': 140,\n",
       "      '94:orange 96:blue': 240,\n",
       "      '94:orange 96:brown': 130,\n",
       "      '94:orange 96:green': 200,\n",
       "      '94:orange 96:orange': 160,\n",
       "      '94:orange 96:red': 130,\n",
       "      '94:orange 96:yellow': 140,\n",
       "      '94:red 96:blue': 480,\n",
       "      '94:red 96:brown': 260,\n",
       "      '94:red 96:green': 400,\n",
       "      '94:red 96:orange': 320,\n",
       "      '94:red 96:red': 260,\n",
       "      '94:red 96:yellow': 280,\n",
       "      '94:tan 96:blue': 240,\n",
       "      '94:tan 96:brown': 130,\n",
       "      '94:tan 96:green': 200,\n",
       "      '94:tan 96:orange': 160,\n",
       "      '94:tan 96:red': 130,\n",
       "      '94:tan 96:yellow': 140,\n",
       "      '94:yellow 96:blue': 480,\n",
       "      '94:yellow 96:brown': 260,\n",
       "      '94:yellow 96:green': 400,\n",
       "      '94:yellow 96:orange': 320,\n",
       "      '94:yellow 96:red': 260,\n",
       "      '94:yellow 96:yellow': 280})"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "MM = joint(bag94, bag96, '94:{} 96:{}'.format)\n",
    "MM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "We observe that \"One is yellow and one is green\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "button": false,
    "collapsed": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Dist({'94:green 96:yellow': 140, '94:yellow 96:green': 400})"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def yellow_and_green(outcome): return 'yellow' in outcome and 'green' in outcome\n",
    "\n",
    "favorable(yellow_and_green, MM)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given this observation, we want to know \"What is the probability that the yellow M&M came from the 1994 bag?\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "button": false,
    "collapsed": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7407407407407407"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def yellow94(outcome): return '94:yellow' in outcome\n",
    "\n",
    "P(yellow94, favorable(yellow_and_green, MM))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "So there is a 74% chance that the yellow comes from the 1994 bag.\n",
    "\n",
    "Answering this question was straightforward: just like all the other probability problems, we simply create a sample space, and use `P` to pick out the probability of the event in question, given what we know about the outcome.\n",
    "But in a sense it is curious that we were able to solve this problem with the same methodology as the others: this problem comes from a section titled **My favorite Bayes's Theorem Problems**, so one would expect that we'd need to invoke Bayes Theorem to solve it.  The computation above shows that that is not necessary. \n",
    "\n",
    "![Bayes](http://img1.ph.126.net/xKZAzeOv_mI8a4Lwq7PHmw==/2547911489202312541.jpg)\n",
    "<center><a href=\"https://en.wikipedia.org/wiki/Thomas_Bayes\">Rev. Thomas Bayes</a><br>1701-1761\n",
    "</center>\n",
    "\n",
    "Of course, we *could* solve it using Bayes Theorem. Why is Bayes Theorem recommended? Because we are asked about the probability of an outcome given the evidence&mdash;the probability the yellow came from the 94 bag, given that there is a yellow and a green. But the problem statement doesn't directly tell us the probability of that outcome given the evidence; it just tells us the probability of the evidence given the outcome. \n",
    "\n",
    "Before we see the colors of the M&Ms, there are two hypotheses, `A` and `B`, both with equal probability:\n",
    "\n",
    "    A: first M&M from 94 bag, second from 96 bag\n",
    "    B: first M&M from 96 bag, second from 94 bag\n",
    "    P(A) = P(B) = 0.5\n",
    "    \n",
    "Then we get some evidence:\n",
    "    \n",
    "    E: first M&M yellow, second green\n",
    "    \n",
    "We want to know the probability of hypothesis `A`, given the evidence:\n",
    "    \n",
    "    P(A | E)\n",
    "    \n",
    "That's not easy to calculate (except by enumerating the sample space, which our `P` function does). But Bayes Theorem says:\n",
    "    \n",
    "    P(A | E) = P(E | A) * P(A) / P(E)\n",
    "    \n",
    "The quantities on the right-hand-side are easier to calculate:\n",
    "    \n",
    "    P(E | A) = 0.20 * 0.20 = 0.04\n",
    "    P(E | B) = 0.10 * 0.14 = 0.014\n",
    "    P(A)     = 0.5\n",
    "    P(B)     = 0.5\n",
    "    P(E)     = P(E | A) * P(A) + P(E | B) * P(B) \n",
    "             = 0.04     * 0.5  + 0.014    * 0.5   =   0.027\n",
    "    \n",
    "And we can get a final answer:\n",
    "    \n",
    "    P(A | E) = P(E | A) * P(A) / P(E) \n",
    "             = 0.04     * 0.5  / 0.027 \n",
    "             = 0.7407407407\n",
    "             \n",
    "You have a choice: Bayes Theorem allows you to do less calculation at the cost of more algebra; that is a great trade-off if you are working with pencil and paper. Enumerating the sample space allows you to do less algebra at the cost of more calculation; usually a good trade-off if you have a computer. But regardless of the approach you use, it is important to understand Bayes theorem and how it works.\n",
    "\n",
    "There is one important question that Allen Downey does not address: *would you  eat twenty-year-old M&Ms*?\n",
    "&#128552;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
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   },
   "source": [
    "<hr>\n",
    "\n",
    "# Simulation\n",
    "\n",
    "Sometimes it is inconvenient, difficult, or even impossible to explicitly enumerate a sample space. Perhaps the sample space is infinite, or perhaps it is just very large and complicated (perhaps with a bunch of low-probability outcomes that don't seem very important). In that case, we might feel more confident in writing a program to *simulate* a random outcome. *Random sampling* from such a simulation\n",
    "can give an accurate estimate of probability.\n",
    "\n",
    "# Simulating Monopoly\n",
    "\n",
    "![Mr. Monopoly](http://buckwolf.org/a.abcnews.com/images/Entertainment/ho_hop_go_050111_t.jpg)<center>[Mr. Monopoly](https://en.wikipedia.org/wiki/Rich_Uncle_Pennybags)<br>1940&mdash;\n",
    "\n",
    "Consider [problem 84](https://projecteuler.net/problem=84) from the excellent [Project Euler](https://projecteuler.net), which asks for the probability that a player in the game Monopoly ends a roll on each of the squares on the board.  To answer this we need to take into account die rolls, chance and community chest cards, and going to jail (from the \"go to jail\" space, from a card, or from rolling doubles three times in a row). We do not need to take into account anything about acquiring properties or exchanging money or winning or losing the game, because these events don't change a player's location. \n",
    "\n",
    "A game of Monopoly can go on forever, so the sample space is infinite. Even if we limit the sample space to say, 1000 rolls, there are $21^{1000}$ such sequences of rolls, and even more possibilities when we consider drawing cards. So it is infeasible to explicitly represent the sample space. There are techniques for representing the problem as\n",
    "a Markov decision problem (MDP) and solving it, but the math is complex (a [paper](https://faculty.math.illinois.edu/~bishop/monopoly.pdf) on the subject runs 15 pages).\n",
    "\n",
    "The simplest approach is to implement a simulation and run it for, say, a million rolls.  Here is the code for a simulation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from collections import deque as Deck # a Deck of community chest or chance cards\n",
    "\n",
    "# The Monopoly board, as specified by https://projecteuler.net/problem=84\n",
    "(GO,   A1, CC1, A2,  T1, R1, B1,  CH1, B2, B3,\n",
    " JAIL, C1, U1,  C2,  C3, R2, D1,  CC2, D2, D3, \n",
    " FP,   E1, CH2, E2,  E3, R3, F1,  F2,  U2, F3, \n",
    " G2J,  G1, G2,  CC3, G3, R4, CH3, H1,  T2, H2) = board = range(40)\n",
    "\n",
    "# A card is either a square, a set of squares meaning advance to the nearest, \n",
    "# a -3 to go back 3 spaces, or None meaning no change to location.\n",
    "CC_deck = Deck([GO, JAIL] +  14 * [None])\n",
    "CH_deck = Deck([GO, JAIL, C1, E3, H2, R1, -3, {U1, U2}] \n",
    "               + 2 * [{R1, R2, R3, R4}] + 6 * [None])\n",
    "\n",
    "def monopoly(rolls):\n",
    "    \"\"\"Simulate given number of dice rolls of a Monopoly game, \n",
    "    and return the counts of how often each square is visited.\"\"\"\n",
    "    counts = [0] * len(board)\n",
    "    doubles = 0 # Number of consecutive doubles rolled\n",
    "    random.shuffle(CC_deck)\n",
    "    random.shuffle(CH_deck)\n",
    "    goto(GO)\n",
    "    for _ in range(rolls):\n",
    "        d1, d2 = random.randint(1, 6), random.randint(1, 6)\n",
    "        doubles = (doubles + 1 if d1 == d2 else 0)\n",
    "        goto(here + d1 + d2)\n",
    "        if here == G2J or doubles == 3:\n",
    "            goto(JAIL)\n",
    "            doubles = 0\n",
    "        elif here in (CC1, CC2, CC3):\n",
    "            do_card(CC_deck)\n",
    "        elif here in (CH1, CH2, CH3):\n",
    "            do_card(CH_deck)\n",
    "        counts[here] += 1\n",
    "    return counts\n",
    "\n",
    "def goto(square):\n",
    "    \"Update 'here' to be this square (and handle passing GO).\"\n",
    "    global here\n",
    "    here = square % len(board)        \n",
    "\n",
    "def do_card(deck):\n",
    "    \"Take the top card from deck and do what it says.\"\n",
    "    card = deck.popleft()       # The top card\n",
    "    deck.append(card)           # Move top card to bottom of deck\n",
    "    if card == None:            # Don't move\n",
    "        pass\n",
    "    elif card == -3:            # Go back 3 spaces\n",
    "        goto(here - 3)\n",
    "    elif isinstance(card, set): # Advance to next railroad or utility\n",
    "        next1 = min({place for place in card if place > here} or card)\n",
    "        goto(next1)\n",
    "    else:                       # Go to destination named on card\n",
    "        goto(card)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
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   },
   "source": [
    "Let's run the simulation for a million dice rolls:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [],
   "source": [
    "counts = monopoly(10**6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "And print a table of square names and their percentages:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "button": false,
    "collapsed": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "JAIL 6.23%\n",
      "E3   3.21%\n",
      "R3   3.09%\n",
      "GO   3.09%\n",
      "D3   3.08%\n",
      "R1   3.00%\n",
      "D2   2.94%\n",
      "R2   2.91%\n",
      "E1   2.85%\n",
      "FP   2.84%\n",
      "U2   2.80%\n",
      "D1   2.78%\n",
      "E2   2.72%\n",
      "C1   2.69%\n",
      "F1   2.69%\n",
      "F2   2.66%\n",
      "G2   2.64%\n",
      "G1   2.64%\n",
      "H2   2.63%\n",
      "F3   2.61%\n",
      "U1   2.61%\n",
      "CC2  2.60%\n",
      "G3   2.48%\n",
      "C3   2.46%\n",
      "R4   2.41%\n",
      "CC3  2.40%\n",
      "C2   2.39%\n",
      "T1   2.34%\n",
      "B2   2.31%\n",
      "B3   2.29%\n",
      "B1   2.26%\n",
      "H1   2.21%\n",
      "T2   2.17%\n",
      "A2   2.15%\n",
      "A1   2.15%\n",
      "CC1  1.88%\n",
      "CH2  1.07%\n",
      "CH3  0.91%\n",
      "CH1  0.82%\n",
      "G2J  0.00%\n"
     ]
    }
   ],
   "source": [
    "property_names = \"\"\"\n",
    " GO,   A1, CC1, A2,  T1, R1, B1,  CH1, B2, B3,\n",
    " JAIL, C1, U1,  C2,  C3, R2, D1,  CC2, D2, D3, \n",
    " FP,   E1, CH2, E2,  E3, R3, F1,  F2,  U2, F3, \n",
    " G2J,  G1, G2,  CC3, G3, R4, CH3, H1,  T2, H2\"\"\".replace(',', ' ').split()\n",
    "\n",
    "for (c, n) in sorted(zip(counts, property_names), reverse=True):\n",
    "    print('{:4} {:.2%}'.format(n, c / sum(counts)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "There is one square far above average: `JAIL`, at a little over 6%. There are four squares far below average: the three chance squares, `CH1`, `CH2`, and `CH3`, at around 1% (because 10 of the 16 chance cards send the player away from the square), and the \"Go to Jail\" square, which has a frequency of 0 because you can't end a turn there. The other squares are around 2% to 3% each, which you would expect, because 100% / 40 = 2.5%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Central Limit Theorem \n",
    "\n",
    "We have covered the concept of *distributions* of outcomes. You may have heard of the *normal distribution*, the *bell-shaped curve.* In Python it is called `random.normalvariate` (also `random.gauss`). We can plot it with the help of the `repeated_hist` function defined below, which samples a distribution `n` times and displays a histogram of the results. (*Note:* in this section I am using \"distribution\" to mean a function that, each time it is called, returns a random sample from a distribution. I am not using it to mean a mapping of type `Dist`.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline \n",
    "import matplotlib.pyplot as plt\n",
    "from statistics import mean\n",
    "from random import normalvariate, triangular, choice, vonmisesvariate, uniform\n",
    "\n",
    "def normal(mu=0, sigma=1): return random.normalvariate(mu, sigma)\n",
    "\n",
    "def repeated_hist(dist, n=10**6, bins=100):\n",
    "    \"Sample the distribution n times and make a histogram of the results.\"\n",
    "    samples = [dist() for _ in range(n)]\n",
    "    plt.hist(samples, bins=bins, density=True)\n",
    "    plt.title('{} (μ = {:.1f})'.format(dist.__name__, mean(samples)))\n",
    "    plt.grid(axis='x')\n",
    "    plt.yticks([], '')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x106ae1438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Normal distribution\n",
    "repeated_hist(normal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Why is this distribution called *normal*? The **Central Limit Theorem** says  that it is the ultimate limit of other distributions, as follows (informally):\n",
    "- Gather *k* independent distributions. They need not be normal-shaped.\n",
    "- Define a new distribution to be the result of sampling one number from each of the *k* independent distributions and adding them up.\n",
    "- As long as *k* is not too small, and the component distributions are not super-pathological, then the new distribution will tend towards a normal distribution.\n",
    "\n",
    "Here's a simple example: summing ten independent die rolls:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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S4Cr+f2zxbIZx5KnWfCzwJuB+DG/s76iqlyd5IBOteVaSTcAfVNXpU645ySMZesUwfJR/\na1X9yZRrBkhyPHAusA/wReDXGF/nrGDNfnVakprwm3qS1ISBLElNGMiS1ISBLElNGMiS1ISBLElN\nGMiS1MT/AekMsW/hANdAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x124ad9748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sum10dice(): return sum(random.randint(1, 6) for _ in range(10))\n",
    "\n",
    "repeated_hist(sum10dice, bins=range(10, 61))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As another example, let's take just *k* = 5 component distributions representing the per-game scores of 5 basketball players, and then sum them together to form the new distribution, the team score. I'll be creative in defining the distributions for each player, but [historically accurate](https://www.basketball-reference.com/teams/GSW/2016.html) in the mean for each distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def SC(): return max(0, normal(12.1, 3) + 3 * triangular(1, 13, 4))                     # 30.1\n",
    "def KT(): return max(0, triangular(8, 22, 15.3) + choice((0, 3 * triangular(1, 9, 4)))) # 22.1\n",
    "def DG(): return max(0, vonmisesvariate(30, 2) * 3.08)                                  # 14.0\n",
    "def HB(): return max(0, choice((normal(6.7, 1.5), normal(16.7, 2.5))))                  # 11.7\n",
    "def BE(): return max(0, normal(17, 3) + uniform(0, 40))                                 # 37.0\n",
    "\n",
    "team = (SC, KT, DG, HB, BE)\n",
    "\n",
    "def Team(team=team): return sum(player() for player in team)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWQAAAEICAYAAABoLY4BAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFG7+33uq9XcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b0239e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11cac1b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWQAAAEICAYAAABoLY4BAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c7dc400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x106c39860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWQAAAEICAYAAABoLY4BAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSWrCQpakJv4PEqD2OJabj0QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11ce4abe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for player in team: \n",
    "    repeated_hist(player, bins=range(70))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that none of the players have a distribution that looks like a normal distribution: `SC` is skewed to one side (the mean is 5 points to the right of the peak); the three next players have bimodal distributions; and `BE` is too flat on top. \n",
    "\n",
    "Now we define the team score to be the sum of the *k* = 5 players, and display this new distribution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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IvDkidm+7g2OBu+hH7dNmq/VK4LciYlVEHAL8LPCdDurbqYg4jmYM9tcz8/8GVpWuPzM3\nZea+mbk+M9fTBNwR7euhdO2tr9Ic2CMiDqU5GL+NftT+MPCO9voxwL3t9dHX3tXRzEUeCT0cuBW4\ng+YH/Spgb+Ab7ZN1A7BX13XOUvtZwN3AZuBCmiO0JWsHLqYZ636aJgB+f2e1Ap+gOdJ8D+1R6YL1\n30cz7vfd9nJ+xfqH1T5j/QO0syz6UDtNAH+p/b2/HTimR7W/FbiNZkbFLcCRS1W7b52WpCJ6N2Qh\nSePKQJakIgxkSSrCQJakIgxkSSrCQJakIgxkSSri/wHHthX0iOivnwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c4daac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "repeated_hist(Team, bins=range(50, 180))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sure enough, this looks very much like a normal distribution. The **Central Limit Theorem** appears to hold in this case. But I have to say: \"Central Limit\" is not a very evocative name, so I propose we re-name this as the **Strength in Numbers Theorem**, to indicate the fact that if you have a lot of numbers, you tend to get the expected result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "button": false,
    "deletable": true,
    "new_sheet": false,
    "run_control": {
     "read_only": false
    }
   },
   "source": [
    "# Conclusion\n",
    "\n",
    "We've had an interesting tour and met some giants of the field: Laplace, Bernoulli, Fermat, Pascal, Bayes, Newton, ... even Mr. Monopoly and The Count.\n",
    "\n",
    "The conclusion is: be methodical in defining the sample space and the event(s) of interest, and be careful in counting the number of outcomes in the numerator and denominator. and you can't go wrong. Easy as 1-2-3. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "# Appendix: Continuous Sample Spaces\n",
    "\n",
    "Everything up to here has been about discrete, finite sample spaces, where we can *enumerate* all the possible outcomes. \n",
    "\n",
    "But a reader asked about *continuous* sample spaces, such as the space of real numbers. The principles are the same: probability is still the ratio of the favorable cases to all the cases, but now instead of *counting* cases, we have to (in general) compute integrals to compare the sizes of cases. \n",
    "Here we will cover a simple example, which we first solve approximately by simulation, and then exactly by calculation.\n",
    "\n",
    "## The Hot New Game Show Problem: Simulation\n",
    "\n",
    "Oliver Roeder posed [this problem](http://fivethirtyeight.com/features/can-you-win-this-hot-new-game-show/) in the 538 *Riddler* blog:\n",
    "\n",
    ">Two players go on a hot new game show called *Higher Number Wins.* The two go into separate booths, and each presses a button, and a random number between zero and one appears on a screen. (At this point, neither knows the other’s number, but they do know the numbers are chosen from a standard uniform distribution.) They can choose to keep that first number, or to press the button again to discard the first number and get a second random number, which they must keep. Then, they come out of their booths and see the final number for each player on the wall. The lavish grand prize — a case full of gold bullion — is awarded to the player who kept the higher number. Which number is the optimal cutoff for players to discard their first number and choose another? Put another way, within which range should they choose to keep the first number, and within which range should they reject it and try their luck with a second number?\n",
    "\n",
    "We'll use this notation:\n",
    "- **A**, **B**: the two players.\n",
    "- *A*, *B*: the cutoff values they choose: the lower bound of the range of first numbers they will accept.\n",
    "- *a*, *b*: the actual random numbers that appear on the screen.\n",
    "\n",
    "For example, if player **A** chooses a cutoff of *A* = 0.6, that means that **A** would accept any first number greater than 0.6, and reject any number below that cutoff. The question is: What cutoff, *A*, should player **A** choose to maximize the chance of winning, that is, maximize P(*a* > *b*)?\n",
    "\n",
    "First, simulate the number that a player with a given cutoff gets (note that `random.random()` returns a float sampled uniformly from the interval [0..1]):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "number= random.random\n",
    "\n",
    "def strategy(cutoff):\n",
    "    \"Play the game with given cutoff, returning the first or second random number.\"\n",
    "    first = number()\n",
    "    return first if first > cutoff else number()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7567488540951384"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "strategy(.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now compare the numbers returned with a cutoff of *A* versus a cutoff of *B*, and repeat for a large number of trials; this gives us an estimate of the probability that cutoff *A* is better than cutoff *B*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Pwin(A, B, trials=20000):\n",
    "    \"The probability that cutoff A wins against cutoff B.\"\n",
    "    return mean(strategy(A) > strategy(B) \n",
    "                for _ in range(trials))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5668"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pwin(0.6, 0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now define a function, `top`, that considers a collection of possible cutoffs, estimate the probability for each cutoff playing against each other cutoff, and returns a list with the `N` top cutoffs (the ones that defeated the most number of opponent cutoffs), and the number of opponents they defeat: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def top(N, cutoffs):\n",
    "    \"Return the N best cutoffs and the number of opponent cutoffs they beat.\"\n",
    "    winners = Counter(A if Pwin(A, B) > 0.5 else B\n",
    "                      for (A, B) in itertools.combinations(cutoffs, 2))\n",
    "    return winners.most_common(N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.6100000000000001, 44),\n",
       " (0.60000000000000009, 43),\n",
       " (0.63000000000000012, 43),\n",
       " (0.55000000000000004, 42),\n",
       " (0.58000000000000007, 42),\n",
       " (0.56000000000000005, 42),\n",
       " (0.62000000000000011, 42),\n",
       " (0.64000000000000012, 41),\n",
       " (0.65000000000000013, 41),\n",
       " (0.57000000000000006, 40)]"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from numpy import arange\n",
    "\n",
    "top(10, arange(0.5, 1.0, 0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We get a good idea of the top cutoffs, but they are close to each other, so we can't quite be sure which is best, only that the best is somewhere around 0.60. We could get a better estimate by increasing the number of trials, but that would consume more time.\n",
    "\n",
    "## The Hot New Game Show Problem: Exact Calculation\n",
    "\n",
    "More promising is the possibility of making `Pwin(A, B)` an exact calculation. But before we get to `Pwin(A, B)`, let's solve a simpler problem: assume that both players **A** and **B** have chosen a cutoff, and have each received a number above the cutoff. What is the probability that **A** gets the higher number? We'll call this `Phigher(A, B)`. We can think of this as a two-dimensional sample space of points in the (*a*, *b*) plane, where *a* ranges from the cutoff *A* to 1 and *b* ranges from the cutoff B to 1. Here is a diagram of that two-dimensional sample space, with the cutoffs *A*=0.5 and *B*=0.6:\n",
    "\n",
    "<img src=\"http://norvig.com/ipython/probability2da.jpg\" width=413>\n",
    "\n",
    "The total area of the sample space is 0.5 &times; 0.4 = 0.20, and in general it is (1 - *A*) &middot; (1 - *B*). What about the favorable cases, where **A** beats **B**? That corresponds to the shaded triangle below:\n",
    "\n",
    "<img src=\"http://norvig.com/ipython/probability2d.jpg\" width=413>\n",
    "\n",
    "The area of a triangle is 1/2 the base times the height, or in this case, 0.4<sup>2</sup> / 2 = 0.08, and in general, (1 - *B*)<sup>2</sup> / 2. So in general we have:\n",
    "\n",
    "    Phigher(A, B) = favorable / total\n",
    "    favorable     = ((1 - B) ** 2) / 2 \n",
    "    total         = (1 - A) * (1 - B)\n",
    "    Phigher(A, B) = (((1 - B) ** 2) / 2) / ((1 - A) * (1 - B))\n",
    "    Phigher(A, B) = (1 - B) / (2 * (1 - A))\n",
    "    \n",
    "And in this specific case we have:\n",
    "\n",
    "     A = 0.5; B = 0.6\n",
    "     favorable         = 0.4 ** 2 / 2 = 0.08\n",
    "     total             = 0.5 * 0.4    = 0.20\n",
    "     Phigher(0.5, 0.6) = 0.08 / 0.20  = 0.4\n",
    "\n",
    "But note that this only works when the cutoff *A* &le; *B*; when *A* > *B*, we need to reverse things. That gives us the code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Phigher(A, B):\n",
    "    \"Probability that a sample from [A..1] is higher than one from [B..1].\"\n",
    "    if A <= B:\n",
    "        return (1 - B) / (2 * (1 - A))\n",
    "    else:\n",
    "        return 1 - Phigher(B, A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Phigher(0.5, 0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're now ready to tackle the full game. There are four cases to consider, depending on whether **A** and **B** gets a first number that is above or below their cutoff choices:\n",
    "\n",
    "| first *a* | first *b* | P(*a*, *b*) | P(A wins &vert; *a*, *b*) |  Comment |\n",
    "|:-----:|:-----:| ----------- | ------------- | ------------ |\n",
    "| *a* > *A* | *b* > *B* | (1 - *A*) &middot; (1 - *B*) | Phigher(*A*, *B*) | Both above cutoff; both keep first numbers |\n",
    "| *a* < *A* | *b* < *B* | *A* &middot; *B* | Phigher(0, 0)  | Both below cutoff, both get new numbers from [0..1] |\n",
    "| *a* > *A* | *b* < *B* | (1 - *A*) &middot;  *B* | Phigher(*A*, 0) | **A** keeps number; **B** gets new number from [0..1] |\n",
    "| *a* < *A* | *b* > *B* | *A* &middot; (1 - *B*) | Phigher(0, *B*) | **A** gets new number from [0..1]; **B** keeps number |\n",
    "\n",
    "For example, the first row of this table says that the event of both first numbers being above their respective cutoffs has probability (1 - *A*) &middot; (1 - *B*), and if this does occur, then the probability of **A** winning is Phigher(*A*, *B*).\n",
    "We're ready to replace the old simulation-based `Pwin` with a new calculation-based version:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def Pwin(A, B):\n",
    "    \"With what probability does cutoff A win against cutoff B?\"\n",
    "    return ((1-A) * (1-B) * Phigher(A, B)  # both above cutoff\n",
    "            + A * B       * Phigher(0, 0)  # both below cutoff\n",
    "            + (1-A) * B   * Phigher(A, 0)  # A above, B below\n",
    "            + A * (1-B)   * Phigher(0, B)) # A below, B above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.495"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pwin(0.5, 0.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Pwin` relies on a lot of algebra. Let's define a few tests to check for obvious errors:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'ok'"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def test():\n",
    "    assert Phigher(0.5, 0.5) == Phigher(0.75, 0.75) == Phigher(0, 0) == 0.5\n",
    "    assert Pwin(0.5, 0.5) == Pwin(0.75, 0.75) == 0.5\n",
    "    assert Phigher(.6, .5) == 0.6\n",
    "    assert Phigher(.5, .6) == 0.4\n",
    "    return 'ok'\n",
    "\n",
    "test()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat the calculation with our new, exact `Pwin`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.62000000000000011, 49),\n",
       " (0.6100000000000001, 48),\n",
       " (0.60000000000000009, 47),\n",
       " (0.59000000000000008, 46),\n",
       " (0.63000000000000012, 45),\n",
       " (0.58000000000000007, 44),\n",
       " (0.57000000000000006, 43),\n",
       " (0.64000000000000012, 42),\n",
       " (0.56000000000000005, 41),\n",
       " (0.55000000000000004, 40)]"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top(10, arange(0.5, 1.0, 0.01))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is good to see that the simulation and the exact calculation are in rough agreement; that gives me more confidence in both of them. We see here that 0.62 defeats all the other cutoffs, and 0.61 defeats all cutoffs except 0.62. The great thing about the exact calculation code is that it runs fast, regardless of how much accuracy we want. We can zero in on the range around 0.6:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.6180000000000001, 199),\n",
       " (0.6170000000000001, 198),\n",
       " (0.6160000000000001, 197),\n",
       " (0.61900000000000011, 196),\n",
       " (0.6150000000000001, 195),\n",
       " (0.6140000000000001, 194),\n",
       " (0.6130000000000001, 193),\n",
       " (0.62000000000000011, 192),\n",
       " (0.6120000000000001, 191),\n",
       " (0.6110000000000001, 190)]"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top(10, arange(0.5, 0.7, 0.001))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This says 0.618 is best, better than 0.620. We can get even more accuracy:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(0.61803400000002973, 2000),\n",
       " (0.6180330000000297, 1999),\n",
       " (0.61803200000002967, 1998),\n",
       " (0.61803500000002976, 1997),\n",
       " (0.61803100000002964, 1996),\n",
       " (0.61803000000002961, 1995),\n",
       " (0.61802900000002958, 1994),\n",
       " (0.61803600000002978, 1993),\n",
       " (0.61802800000002955, 1992),\n",
       " (0.61802700000002952, 1991)]"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top(10, arange(0.617, 0.619, 0.000001))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So 0.618034 is best. Does that number [look familiar](https://en.wikipedia.org/wiki/Golden_ratio)? Can we prove that it is what I think it is?\n",
    "\n",
    "To understand the strategic possibilities, it is helpful to draw a 3D plot of `Pwin(A, B)` for values of *A* and *B* between 0 and 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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I7e1CvpeC3WKC1cjDYhLQ7bTAahLQ77Gi32PDgNcKp8XY6JfH5KQiolk5q/epmjhSjhAh\ncdTckBgiGsJJTNKHUa80mSzLWFhYwPb2Nl566SU8e/asruKEPEPNTzydx8TaLiZWS//tpLJ4sr6H\n8tva6zJjYzepesxFN4/5eEq1bXTYi7uLUdW2f3IpgHxRxgtBD14IenBzwIM+j7Wmr+c4dGpk6ChY\n4giAbr4aDZ9tHkgMEXXlNCbpw6hHZCibzWJiYgJutxtjY2Pgeb7uXiUSK2wa+Z4UihLuLsbw1swW\n1mJpvPl0u/I3i4FHoShBeXrdLgs2drOq5zAZBABF1bZ0Jqc7VixdwORaHO/MRyrbPvh8FwJOCz50\npRvvu9QNu7n+t/N2EUMAahrhUpbrA2pxdJjnqF3e21aAxBBRN05rkj6MWouEra0tzM7O4urVq/D7\n/XU7rhaKDFWnngtGtlDEt2a28feTG3h7bgfJnAgACHosqv0GfTbMbiVU20yCfrHNiPr3PJLK67aF\n42ndtmdbCXxrZgt/c28ZRoHHyLAP/+WtAfzg9T54bKYTva7T0i6l9fVGK44A6NJq2hEiJI5qC4kh\nouac1SR9GLW6ORSLRczMzCCTyWBsbAwmk3pxqbdXiW6CjeXhShz/6cEa/n5yA1d7nbi7FKv8zWbi\nsRbPqPZ3W/W31vS+cFKynVJvc5oFbCULqm0ei4CoRiDZTDzWdw+OWShK+P5cBFNrcfy7Lz/Ch6/2\n4L96OYQPPN8NA0OEnRftUlrfDHCcfvhsoVBQ3TdJHNUOEkNETTlsrlizkkwmMTExgf7+fly9epV5\nzhQZan8y+SL+fnIdf/r2Iua2D3w9uxm1WBn02jC9oY4CFRlv5WpMLZj6XBaVoAGAAZ8NT9f31Nv8\nDsRW46ptXTYeS3F1eq3bacbWXikN97XH6/ja43X4HWb8168M4yfGhxFwqqNX50E7pcmaDZY4EkVR\nJY6UXbJJHJ0NEkNEzShHg85qkq4XsixjdXUVKysreOGFF+B0Oqvu24j+RiRW6kM8nccX3lnGX7y7\ngotddpUQ4jlgJaZOWTkt+tvoTlLt++lxmrG5p/YLdbvMOjHkYPh+rEZBt63L48JSfEf9WKGILc1+\nHIDPff0p/vCtGXzs5RB++gOXMBxw6J7vtJAYqh/Vhs+Kolj5HGRZhslkgtlsphEiJ4TEEHHunLdJ\nuh4UCgU8fvwYBoMBr7zyiuoXGYtGpMlqLYY6XWxt72XxR99dxN/cX0WmUPpste/JgNeKlahawBQl\n9T4WA481TRSox23RiSEjI30lMkJK2UJRvx/j2vN7XJiPqQWS2wxEEkBOlPBX7y7iS3cW8cM3B/Bz\nP/A8rvSdvVFou5TWtyIscfTs2TN4PB74fD4ANF/tJJAYIs6VWpika00sFsOTJ0/w3HPPobe391iP\nacc0WaeSzon4k+8u4qtPNjEfUZe5x9LqlFjAbtaJoe2EOgrEMk+bGcInldd7iLYSWd22dY0fCUAl\nHaZ6PoYnyW2zADjYV5KBJ2s7+Ke/84/42Esh/Msfvo5e9+lL9NshMtQuPwLKP9BMJhMEQah0yc5k\nMjR89hiQGCLOBa1JuhV+LcqyjLm5OUSjUbz88suwWo+/KLSbGOpExKKEv76/ht99ax7RVB4vBtWR\nEiPPYSWqTokJvHrxsBp5hDVixcUwT7OEijZ65DALurSZz2ZCRJNys5v0+5WeT19xltMHleAyC5Bk\n4G/vL+P1hyv48dt9+Pkfuo4uT/W0cDXaoZqsHQRdGWWkrvxjtPzvauJodnYWPT09GBgYaNh5NwPN\nv2IRTY8sy4hGo1hZWWmZtFgmk8GdO3cAAKOjoycSQkBjxNBZ/n6c5+8ksXVnMYqf+X/u4X977Wml\nUssoqN/DQZ8VoiYFtpfVmKd9Nmh20f0bgE4w9brM2NMYsYNeG7QfQZ9Xf10O+vT79bgsOmN36bh6\ngaSsjMwXZXzxXhg/84ffxmf+8k1MTU1hfX1dNa39MNqhmqydUn3FYrFqir98b1b2MZIkCV/4whfw\n4MGDOp9p80GRIeJMlL1BuVwO8Xgc/f39jT6lI9nc3MSzZ89w7dq1Sm79pFDTxdZkN1PAZ746g9cm\n1nWCIqEROqVePQdpMw7QpchcDPN0NKWO5HQ7Tdja02xjNGB0MEZusMzTrP16XRZsaqJFXU4Ttvf0\nDRx3GH2MvC4H/uR+BO9FgJ9/Pw/H1hZyuRycTmdltprFoq9Ga4eoSjuJIUmSjvQ7lilHjjKZDGw2\nW43PrPkhMUScCq1J2mAw1H1gapmyUDjqplwsFvH06VPk83mMj4/DaDz9vKd6G6gBGtTK4iTn/Prk\nBn7rjWnspPK4GLBjflvpD5KxyvDmKAl6rViJHW6eNhs4rEa1USCrTgyZDCzztP56Oq552sh4vj63\nTSeGTAKHtWhKt29x/znvL8fwyfAu/sWHr+CfffAGctk0YrEYpqenmeKIxFBzUSwWT/xa0uk07HZ7\njc6odSAxRJwYlkm6EdPjy5SFyWG/iBKJBCYnJxEMBhEMBlsurUQG6uocde7RVB6/8+Yz/NW9tco2\nj00thAc8Vl3jRG2jw4DDrBNDWvN00GvD3LZ6/piZIVRYDRiPa57WHrPa87GOO+h3YG5rT7d9W3Hs\nvCjhc1+fwpNwHJ/8oWu4NjSEoaEhSJKEZDKpEkccx8HtdsPj8TAjR61AO/ieyhyWJqsGiaESJIaI\nY3NYyXwjxVD52KybgCzLWFlZwdraGl544QU4HOfTY6XZxNB5/EJvxcjQUXz32Q5+9W8fw2/XRAE1\nLzXgMKvEkIEHVmOHm6ctDPN0eQyG02KA32GG02yAzSRgdNiLUqINgCxD4IDRYR8SiT04nS5wkJET\nJZgEHpFkDsmcWNU8zfIBac8VANJ5fVRJKwIBwGYSEGY8fjedx8c/9yb+1Y/cwE994DJ4nofL5YLL\n5aqIo+npaYiiWIm4Op1OeL1eeL1emM1m3XM2I+0UGTrNfYDEUAkSQ8SxOKqTdKPFEGshz+fzmJyc\nhMViwfj4+Il/MR11zHbrM9RO5EUJn/36LP7fd1YAyEhrythjaXXUR2ee9toxH1FHeHTmaa8Nyzsp\nDPpscFsNKMqAWQBsRh6JTAGJfUOz22pQmZt1nad3dnC114kpRedpp9mAy70OhEQ7BK50vss7aQz6\nbHi6oY7s9DD8QgC7uox1DQ367Jhe39Vtj6fzKBQl/NZrE/j2zCZ+8+Nj6FJ0seZ5HmazGS6XC4FA\nAJIkIZFIIBaLYWpqqmXEUTuYwJWQGDodJIaIQznuXLFmSJMp2dnZwdOnT3H58mV0d3fX5Zi1hMZx\nHJ/FnRR++a8n8HSjJGYGvTZV1+hSybxaPGjN0167ETgYEA8OpXEaAsfhuS47XFYjrAYO81sJPFP0\nFAp5raqITK/LjA1NT6AexhgOrSk6kRNRlIAHS9HKNgPPIeC0YMxiRDydx9x2ApLMFkNdTjO2Gb2I\ntJEmAHAyDNkCB6zsHIjBt2e38GOf/Rp+6+Nj+MCVg15cyhQTz/Nwu91wu92Vv2nFkcvlqniOmkUc\ntVNk6DSQGCpBYoioijYtdtgvjkZHhsrHliQJc3NziMfjGBkZqZmPodlK64kSb05v4y/urFSEEAD4\nHUasHMxVxaDPdrR5WvHRmg08Xgy6kRMlzG8nMbNZEj8vDbpRVFwDFqN+YGuP26oTQwaD/rPMi/rv\njjaaJUoyEtkCHi6XXozbasSFbge8NhPMBh45xXP0ua06MVTqjK2PFrGM20G/HYsa71Mslcer35jC\nw6UdfPK/uF75DlQTEq0ijjpdDGWz2Zb1e50nJIYIJpIkIZ/PH3uuWKPFkCzLSKfTmJiYQCAQwOjo\naE0FRDOW1p/FN9TqkSFZlvG731zAq99awItBl+pvguY98ViPNk/HMnlc6XHCbhYwvZFAoSjj4Yp6\nWOqWxsgc8tkwoxnYqk2/Aaikz5QwmyhG9cJlU1GOv5sp4L2lGK71uWDiedwY8iCRLWB2M8GsVhv0\n2zG7qTdPs4zbfrtZJ4aAUufr//vrU3i6vovf/PjYia65w8TRkydPUCgU4HK54PV64fF46iaOOl0M\nAa3RJLfWkBgiVJx2rlij02Sbm5tYX1/H9evX4fV663LMZhnUWharrSxmzkKmIOEX//IR/nG6lNeK\nJNV+oL2sOsIia9zTSvO002zA1T4HVqIZzO+qB7QqcZgFhHe1PYf06SZt+o2DrOtq7bWZdOM1elxm\nbGrK4t1WIzZ0oknGyk4KyZyI+4ullNqA1wqH2QCH2YCkosrMZdWfn8NswDrDkM2iZLQuvSffeBzG\nxz/3j/ilD/Shp+d0AlwpjoaHh1XiKBwO100ctYsYOs33v1PvGSxIDBEVzjJXrFFpHFEUEY/Hkcvl\nztw76CSQZ6g5WItn8Kv/uIO1RGnR147H4KGfMh9LqQWKUeDQ6zJjwGPF4/AuIsk81jUNEbXdnQd9\nNpXhGdCnm1jCJ+izYWVHva3fa9U1aux1W3ViKOi1YVdj/B7w2LEWU/cNWotlkMgWIMsyRi/4sRRJ\nYTuRhcT4fINeG54yzNNagzlQiixNhw/2nd9K4FNfSeG3LE780ItnH/rKEkd7e3uIx+MIh8MQRbGS\nVjtPcdQuYugkDRe1UBqexBCB45ukm429vb1KtdilS5fqJoQA8gw1AxNre/iNN+YrQggABr1WzGwe\npHeCPguWFWZpk8BhVdEraNBrhYHnsLmXqwggryaCIvDAskbAOMz6W6d2Kn1QY9wGgIDDohNDrC7T\nRsaiZjPpt3W5zDox1Ou2YmO3dIy7CzsQeOClkBdiUX+9srpZG3gOKzv6xoysyFe6IOEzb0whmpXx\nE69c1P39LPA8XxE+SnFUjhwpxZHX61WNGTkJ7SKGTtNwEaB7SxkSQx2OLMsoFAooFostI4JkWcbS\n0hLW19dx69YtrKys1D2q0aqRlGq02uv51mwEv/TXk3i+Wz27Szsew283q8TQoM+Gua0Uup1mDHgs\neLgSRySpjppo430hrx0LmjL7nKju4eO0GHTRpIDTrBND2nQbAGQY0+uTWb2vKMPoG2RgPGGv21IR\nQwBQlIDpjT3kCiJeHvJhJZquNFksMMzTIb8dc1sJ3XaWydskAKvRNP6XL93DRjyNf/mRm7p9zgul\nOAJQVRyV02rHFUftJIZOGhkSRfFcW460MiSGOpiTmqSbgVwuh8nJSdhsNrzyyivgeb7uZmag/gbq\no2imc6k1X3oQxqdfe1oaoqp52drBqlqt4LMZ4Rny4NFKHFuJLAa96sgRAEQ0xmif3YiFiGqTTvgM\nem14klGnm3jG9ynOmAu2qkmlcQCWGSMzWJVgrOczMEzbIb8dT8Nx3F/cgdnAY/SCH9Pru8z+RB6b\nGYBeDG3t6fftdZqwHC+9X7/3jSls7mbw7/7pCAxC7cXFYeJobW3t2OJIkiQYDK2/FJ5G1KXTaZpL\ntk/rXwHEiTmtSbrRRCIRTE9P4/nnn0dXV1dleyPM242YTVaNcDiM2dlZGAyGSsrA4/Gc6AbfKpGh\nP/j2Av7Dm/OVf0fT6giKdlRF2evDc8BLgx5IEnBv+aDOPuBQR46sjPJ47dvitRl1x2GlsOIZtVAx\n8ByWteZpC4eodnq9z6bzGnW7zNjSCDCBZ4um3bQ+qqRM6+VECXfnI+hzWzHgs2FrLwOlhtQazAHA\naTUyR4PYTep7x9/cXcR2IovP/jf/GeyMtFot0YqjYrFY8RwdJo46OTKUSqVIDO1DYqjDOItJulFI\nkoTZ2VkkEgmMjo7qjJONECbNIB6KxSKmpqYgiiLGxsYAALu7u4jFYlhcXATHcRVx5Ha7Wz4c/ttf\nncXrkxuVf5sFDuHdA1FiN/EIxw8Eg8ABK7EMLgRs4MHh3lIcg151PxXt1R/y2zC9oU6J7WjMzf0e\nq85grE2bCTx03qCQ34b5LfVz+6wCohn1tRtwmHViqNdl1YmhkM+OBU35u8ABK1F9SXxe1KfYvHYz\n7sxHcKnbhaIsY3E/FRhlNGYc9NrwhGGq1kbiAODb0xv4xT97G//+v3sf05NULwRBqHS/BtTiaHV1\nFcViES6XC4VC4dR+o2biNKKOJtYfQGKoQ6iXSfq8p1in02k8evQIPT09GBkZqdr9utM8Q8lkEhMT\nExgYGMA+n51ZAAAgAElEQVTg4CAKhVL1kN/vh9/vBwAUCgXE43FEIhHMzc3BYDBUFgen06m6cTb6\n9RyGLMv4jTdm8cbjTUQVC/Kgz4ZniuaJQY8V0wrz9KDPCr/dhAfLcUgyO+oT00RlnGb14m0x8Lop\n9KwokDZqMuTTj/Pw2vQLLiOjpZuBBrCHrvrsJixsq7cN+u0VUXPY+QGAzVx6Hc+29iBwHEaH/Zjd\n3MMqI9pkZxjGASCW0fud+jxWfHdmEz/zB9/EH/7sB+FmvO5GoBRHFy5cqIij+fl5LC8vY3V1tTJ0\n9iSeo2aBIkNng8RQB1Avk3R5QT2v5w+Hw1hcXMSNGzcqjdqqHbfekaFGeobK78vNmzfhcrmq7mc0\nGtHV1VVJKeZyuYrZNJFIwGw2VxaHZhVCkizj116bxl/fD+Nmn1MlhtxW9e3LqTBPX+lxwG834u25\ng3EWIZ9aLBl46CIwWkPxoM+G2U21f0bbGdpv1w9U9dpNlXEeJoGH2cjDwHG6TtGZgv59Z5W1a/sV\nAfr0HQD4HWadGPLZzdhO6MWQ0rhdlGXcWYjgZtCDoiRjKqz2P+UK+siS02LATkp/Xj0uK9ZjaUys\nRPHTf/AW/viffwhee3OM3lBSFkculwt+vx9ut7viOSpHjlpJHFFk6GyQGGpz6mmSLnt3zpp/F0UR\nT548AQCMj48f6X1plGeoEU0XJycnIYrisd4XLWazGb29vejtLc2WymQyiMViWF5eRjQahdVqRS6X\ng8/ng9VqbXgKVZJl/NuvTOHLD0upMYvGn6IthCoUZRgFDi8G3bi3FMNLgx7V37UzuEI+G+a21VEQ\n7egMbXUagEppPseVxl48F7AhU7BBlkvpskSmAAGloa25ooy8WEReLCIczyBXkMBxpXJ6q1GAKIl4\nYcADk5EHh1I6azcjguMOxA4HWZdyA4AdRjqLdUn2ey2IJvViSGvcBgCLUcDdhQhGLwTwcDlWEYdh\nRmQp6Ldjai2u225UmKen1uL4qVffwn/8uQ/B72jOkQ/lkSLV0mpacVT2HNWzlcdxOG1kiOaSlSAx\n1KY0wiQtCAKKxeKZKjN2d3fx+PFjDA8Po7+//1iPaVSarJ4CLJlMIpVKYXBwEIODg+ciVKxWK6xW\nK/r7+7GwsFC5kc7NzSGdTqsmjtd7dpEky/jMV59VhBAAZDTRiYimkkqGjH63BXeXSgbpqObveY16\nKqWtDsSQ22rQNTosKjwxLosBz/c4AcjYyxSwGksjHEtjwG3G3cWo6nGSLCMnHjzWbhIq1WCyDKTz\nRXQ5zFiM5hBOHgiK57ocWIok4TQbEPTb4DAbIXDA47C6waPVyGOFkc7aSepHa1gYfYx63RZm6qzc\ni+juQgTDAQckGUhmRUQYIzscZrYY2NMYx2c3dvFTv/cm/vQTP4CAs/kEUbX+PIeJo5WVlaYTR6dp\nukhDWg8gMdSGNMokfZYIjSzLWFxcxObmJm7fvn2i0C3HcSgW9WH8WlLPyFA5LWa1WhEKhWpyDI7j\nYDab0dPTg2AwCFmWK6MRnj59WhmqWV4cap0y+PTr0zojs9IcbdN0mh4LefDeSgyFffFi1jRXBPRN\nEbUdmYNeG3YzB6JD4DgYBA5jw17spPJY2E6iIEmVQallEppxH0rhUybks+s6VvucZixqBI3XXnpf\nEzkRU/sC6KUhL1K5Ap7vccJlMyKSyMFiEHSdoy1GHquM8vtUVu/r6XHZmGJoc+/g8YuRJEwCh/dd\n7sVbU+u6fbWmcaBUtbe8wzBwFyX8sz94C5//+R9sGg9RmcOGzSphiaPd3V3E4/GmEEen+SFKpfUH\nkBhqI7Qm6XqXi55WDGWzWUxOTsLpdGJ8fPzE583zfOU114t6RKOU1WLj4+N49913q+57VnGmFcwc\nx8HlcsHlcmFoaEjXw6VYLJ66jP8oPvP1Z/ir+2F02Q8WzW6nSTUYddBrw/RWEmYDj2GXgGS+UBFC\nQKlya3bzQGh4GFEfbXl8uRP0c112eG1GbOxmdREfo8bcXBq5oRY0IcaoDjsj3cb6icKaIM9zHCRZ\nxoxiyOp//pwfoxf82N7LYmm/W3TI78DMhna0hsw0RLN6Eblt+vL5fFFGKlfA7ZAP0xu7qsaPG4yZ\nZkGfHcsMA3fAYcGDxQj+xR99E3/ycx+GvUpUqRGcNrUvCAJ8Ph98Ph8AvTiSJEnlOaq1OCoWiyce\nUUKRoQNIDLUJsiwjk8lgZmYGV69ebYjf4zRiaHt7GzMzM7hy5QoCgcCpj9tu1WTaarFaf55HvR5l\nD5dyJc7u7i6i0ei5lvG/+q0F/On3luGzGbGtGLja6zKrxJDTYkCf2wwjB0zvZDE6pP51qx0dMeC1\nIq6oHLNpKsv8dhPsZgEDbjPm9svfr/c5deennQ026LPpegex+utkGd2jtxmpp81d/TZW6iuVK+LR\nSilCNRxwIOA0q7w6ZQY8Nt24DkCfygKAQZ9d9/pKxyrgyVocIb8dYhEIx9PwMYbLAiXRwxJD5Qq5\nR8tRfPJPvoPf/9kPwsxI3zWC8+ozVE0clX15sizXVBydtuliufq00yEx1AaUo0GyLCMejzfM+HoS\nMSRJEqanp5FOpzE2NnamtEuj+gzV6pjHrRZrJNobv7aMv5xS8Pl8ujL+avzZOyv43DcXAAD9bgui\nikolk2aht5kEJDMFJHIlkZHV+ImKmv432vlfgz4bnm4k8FyXHU6zEZPhOB4ux1WCSVtObuChEz4B\np1m3jSV8tOkrm0nQbfPYjFjXdIS2GHldxRsAhGPqdNZiJImXQl68NORDNJmrRIu6XBadGBI4YJkx\ne4w1Iw2QK3PKlndScJgNuBn0ApARTesN3NVuPTGF2fuduS38D59/G//hv38/U8DVm1o1Xay3ODqN\ngTqdTtcs9d5qkBhqYbQmaYPB0NAS6eOKoXLUo6+v71yiWO0SGdKmxeo5IuCsr0dbxp/P5xGLxbC+\nvo7p6WlVGb/D4dB95m882cT//tXZyr+1pt+Uogx8JOTBzGaiIoQA6PoHbWlSYkrzNQegx2lGUZIx\nux8F6nOZdSM2tCX0Ib9d1zSRlezS+oV6XRZsaBsm+vWptKDHphuvMeS3Y3pDvV+X04TtPb0QWVXM\nHLs+UKqkY80uG/TrmzUCJVO3lgGvHWuKNFsyJ2JyNYofvN4PIKbbP5bSn5eB53Q+oremwvif/+oO\nfv3j442vWqxTB+rjiqNydPWk4ojGcZwNEkMtSjN2kj5KDMmyjLW1NSwvL59r1KMdSuvrnRarNSaT\nCT09Pejp6QGgLuNPJpOw2WwVcfRoM4cv3l1TDYFQDyWVsRrLQuBKZfOzm0nsKfrueC08YooRFE6z\ngLBGfJTF0s1+FxLZAmKZQkUIAUC3y6IRQ7IuIsNqmqhNYfW6zDrh08MQQ6xKLCujmSNrUnyfx64T\nQwGHWZV2e7Jf8j5+0Y/rA57Kv4FS3yGWGGJ1ru52WVViqMzmbhovDfnwaDmK/QI0GAW96AGAoYAD\nc5t7uu3zm3v4rb97gF/52Mu6v9WTRo3jYImjeDyOeDyOpaUllTg6ji/vNJGhTCZDnqF9SAy1GEqT\ndLPNFTtMlBQKBTx+/BgGg+Hcox6t3nSxGdJitfZAKcv4ZVlGOp1GLBbDWw9m8L9+O44ht/p6WFVE\nevrdFsQzBVztceD+chzX+5x4sn4gfgI2AbHsgXgKem2YWj9olNjjNMFnN8FvN2JirWQwDjjUwsao\nMRQPeKy6aJOkS73pU1g9bqtO+LBSQdo2AUCphF1LjmGoNjHMz/0eq6783SRwuL+0A7Eo40qvG5Is\nY3ZzjzF5rNQ1ep1hiGZ1yC6lzpLYyxQQ8pgQzclIZkUM+R14xhA91Roumgw8/vSb0wj6HPhv/8nz\nzH3qwXl3zT8tgiCoOsiLolgxZB9HHFFk6GyQGGohZFlGPp9vqmiQkmpiKBaL4cmTJ7h48SL6+vpq\nctxW7DN0mrRYs9y4zwLHcbDb7UgWDfg/7y0jIwJZWQBQEjhes3rMQ6/LDCPP4fG+wNGOw9AKGYfi\n70GvFRf8Vnxr9mDsfMBhQiSpTkfFNOmpbqdFJ4a0pfkhRgqLlZaKM0zJ2lQaB/nYk+pZg1hNBn1E\nYCjgwOy+OJnerzK7GfSiIOqv2x4XWwxFGWmvAY+94kNajucRCjhgMxngsbN9f1r/VplEtvS+/Prf\n3ke/x4YfvBlk7lcPmvE7ZTAYjhRHZb+Rx+M5tWeIIkMlmiesQByKKIrI5XJNK4QAvRiSZRlzc3OY\nmZnBSy+9VBMhBDTOQH0Wkskk3n33XbhcLrz44ot19QdVo56CMpkT8fN/8RCbezkYeQ5rioGrg4GD\n6FjAyiGTSmJJMR8so/HypPLqzz4jSrCZBIwOebAez+i8MP0eq+rfRkE/TV77A9tlNei6MLO6U2uF\nCmtSfY/LrBu5EfTZkcqpX1eXy6zrMi3w7D4+rOowt1UvTha29jCzsYuxCwGVL4tVam+qkvbqdqvf\nv+VIEmJRgrFKVCLCGAXC7T8OKPV7+qUvvI2J5R3m44kSZXH03HPPYWRkBLdv34bX60U8HsfDhw8r\nIikSiUAU9VFGFul0Gg6Ho8Zn3hqQGGpyynPFlL2DjlqIG2WiVoqhbDaLO3fuQJIkjI2N1TQU2wjP\n0FkIh8N49OgRbty4gVAodGxhVctUVj3FdVGS8a//9glmtvb74/isKBQPXle5cmzIZ0WRE1Dg1V2L\nlxSl2zxkbCT1TQ9tRh53l2IoyjJ2NcNYtZVpQz6b6viAfj7YoFd//eY0EZaSUVgd3Rny25HX7Ner\nERMA0OXQp5L6GfsN+R2645YEkj6qVGB8J0KB0uPvLETgsRn3K8PY0ashv6PSkVp9PP21Ek3mEElk\ncblXnea1mw1YY1TDBX12lUE9ky/iE3/8TawyxBfBpiyOLl26hJGRkYoPryyO7t69i2fPnh0qjihN\ndgCJoSZGkiTkcrlKtdhxFqxGTh8vi5LNzU3cu3cPzz33HC5fvlxzX1Mjh6aehGKxiMnJSWxtbWF8\nfPzE/qBaf7b1eg//j68/w9vzB5VIHpvaJJzMiniuy4ZoKoe9TAErik7SvU4TkorhpgErj9z+gu21\nGTA25ME7C9HKqA6B05fDaztGe6zq45ciIppSeEbZuTaFNey3wWoS0OU0o99jRchnQ5/bgqDPhi6n\nGU6LAQaBY0ZhWLC8RiwT95DfoWstUDo/vUByKNoFbOxmMbkaw+2QD6mcPvXmrpL2ijL6HjktBjzb\n3MXqThLX+g9mwg36HLpO30Cp5F/LTjKH3/jKfSQZQ2mJ49HV1VURR9rIkVIcxeMlQ/1RkaE33ngD\nV65cwaVLl/Cbv/mbzH3eeust3L59Gzdu3MCHPvShEz22mWh8bJ7QcZa5YuX5YI0yVofDYRiNxjP3\nDjoJjUiTnZRytVgwGEQwGDxVJKbWkaF6iKH/9N46vj27o4puqBZLGTAaeCxtpZApSLjgt2EhciA6\netwWbCiaL/Z6bdjKJHGjx4bFnQx24moPT8hvw7xiGKvAAUsab46o8bSE/HY821JPqi+X9rutRvR7\nrPBYDciJEnrdFiSzIqKpPDw2E55pSu+9NpOuQ3UqW0DQY4XTYoBUyMHpdMAocPA71GmxXUbqi+W/\nYQmkLqeZ2dQxlWMZtwtIZkXcDvnw3vJBx21WVKha6mzQ78CT1Rgy+SLmN3dxM+jF5GoMDkYqEWB3\n3wZK/Yh++Qvfxe/+9IfAMyJQxPFheY7i8ThWV1fxiU98ovID+1vf+hY++MEPwulUNxktFov45Cc/\nia997WsIBoMYGxvDxz72MVy/fr2yTzwexy/8wi/gjTfeQCgUwtbW1rEf22xQZKjJKJukTxINUsLz\nfN3ndAFAIpHAwsICjEYjXnrppboJIaD502TKtNhZyuYbGfU7D95b3cWnX5+uzN8qs60QAC8MODG9\nsYdMofR5+uzqqI3WLG0SeFz2mfB4I41UQYbPrY62GYpqz03IZ0O2oL5WtNVf5UgVzwEXAnaMDnlh\nFDh0OUzYzeQxtb6LdL6I+0sxPF7bw9JOGomsyBQPWp+RSeDwbCuJ1VgaU+t7mI7k8DQcxztz29hJ\nZuF3mHAz6Mb4RR9MAq8zZG/u6v03RcY10cdI65XaBeiFjMduQiJTwHtLUdwO+Srl/KxxG0MBJ/N1\n2k0HoicnSni6FsOtkI9p1gbYxmyg5C9660kY/9cbj5h/J06PwWBAIBDA7du38f3vfx+vvfYaZFnG\nm2++iR/+4R/G+9//fvzKr/wKHjx4AAB49913cenSJVy8eBEmkwk/+ZM/iS9/+cuq5/zzP/9z/PiP\n/3ilcWN3d/exH9tskBhqEsrRoGw2eyaTtCAIdRUGsixjeXkZk5OTCIVCcLvddTd3N2ua7KxpMS2H\niaGzvue1Flqbezn8j381qfPmlAaulsTI1V4HTAKPvGIf7aWs9P9c63UiksxjducgghLX+INsdnUK\nwCCpF2GPzYgNRZWYx2aEwyTgxQE3HGYBC9tJbMQzeLgSV4k2VgprTSMeAg4ztjTRmeGAHQVNuXzI\nb0c54LOTzGFyNY5oMo/Ha3GYBQ63gh6MDPlwscuu61ANsAWS1hcFlBoo7mX0KShRIVjeW4rCZBDw\n8rAfG4znrTZkVdugUpRkTC5HYTLqz8Mk8Mzokt1sqHS7/v1vPMbfv7fEPNZ50sw/omqN1+uFwWDA\nb//2b+N73/seXn/9dXzgAx9AJlP63NfW1jA4OFjZPxgMYm1tTfUcMzMziMVi+PCHP4yRkRF8/vOf\nP/Zjmw0SQ02A0iRdTouddnGrZ5Qkn8/jvffeQyKRwPj4OBwOR0NuLs2YJitXi7nd7qapFmsUObGI\nX/zLiUo5+46ijH3QZ4UkA893O7C4rfe4KOeTlfw/GfAcMDrkwWIkgZXYgdgw8ND1/dGWwzsc6lSA\n1yjBZuRws9eGa70OJDIFPA7v4uFqHHv75f3dLr25Oaopxe9ymHWDX7VVawDgYlR42cz6a6McnUrl\nSzPI7i3uwG4y4FK3A6PDfrj3fU4exnBVQD9DrfQ69D4doDRrTEkkkUU+L2LsQgDaTFW1SM8KQ9z4\nHCbcm9/GrUGfanso4GAOpA35HZAVXZB+9f/7Pp6G9V2uz5PjTqxvZ8prjdvtxo/+6I/ife9737Ef\nK4oi7t27h9deew3/8A//gE9/+tOYmZmp1anWlM6+CpqAskm6WCyeS8l82TNUa6LRKO7cuYP+/n7c\nuHEDgiA0LEXXbJGh80qLaanl66xlZOh33lyo9AiyGDisKgzRTrMBl7rsWI2mkRVlRBWLuN3EY02x\n76DPCptJwJUeB+4uxRDy26EMNIV8NpUXyW016EZsKIe9Xu11ItTtRqEoY3IjhamNBBxG/TR7LRYD\nr6ve6vfqhY82pQcAOYbRWVtSD0BXgQYAZgOPZ5sJ3F2IIJkt4IUBN14MenWpNAPPYYkhTjiGU6fL\naWYOXLWaDLgzv40rfR54FNGgjV196qzfY2NGnPq9dhRlGU/CUdzYr1oDoHo+JQ5Nt+1MvohP/sdv\nIcYwbJ8Xjeo+fd6UswnnycDAAFZWVir/Xl1dxcDAgGqfYDCIj3zkI7Db7QgEAvjgBz+Ihw8fHuux\nzUbrXwUtSjkalMuVbrxniQYpqXVkSJIkzM7O4tmzZ3j55Zcr4xbqcexqNItn6LzTYiyaSfQdhy89\nCOP+8m7l34M+m0rAWAw8NuJZpAsSzAKHFUU/oZDPpuqW3Osyg+eAqY2SsHJqIipaI3FQE5lxmgXE\n03mMhDwY9FrxdH0Pm3s5FBSm5KFu/aT6NY3PZshv15muWRVi2vJ8oDQ/TI2M5Yg+IqbfDyrBUZRk\nTKzGkc6L8NpNGLvgh3PfrDwUcDDFVIQhKgY87LLqct+iqbUYjDyHSz0u+GwmZkpO23eojMlQWl4K\nRRmzG3Fc3a8yE6t8V3MioyIumsJnX3+o6/59XrSTGDrp6zjqMWNjY5idncXCwgLy+Ty++MUv4mMf\n+5hqnx/7sR/Dd77zHYiiiHQ6jXfeeQfXrl071mObjda/CloQSZLOZJI+jFpGhjKZDO7cuQOe5zE2\nNgarVX0TbJQoaQZjcT3SYq1WTfZ0I4Hf+Idnqk7OLkUZ+6DXimfbSST3myKG/DaVyFCacl8edCNf\nlFQpNm2/naLm2lPO+vLYjHg55AEHGfeWYliJpsFzwJKmhN6k6eDrNAvYSqqjHkbov1/aAasmgatM\nji/T67boBFKf06gaQguUBrtqDcYGnlP1Vyqzl8ljO5HFnYUICsUiRi/40evWp8NsJoGZyjIY9EuA\nwKl7OW0nsljc2sOtkE+3b3l/FspquJwoYTGyh8u9LmwyoksAmDPQAODtmXV87qsT7IOckXYSQ6fp\nPn1YjyGDwYDPfe5z+MhHPoJr167hJ37iJ3Djxg28+uqrePXVVwEA165dw4/8yI/g1q1bGB8fx8/+\n7M/i5s2bVR/bzHSukaEBKOeKAahJJ+laCZKNjQ3Mzc3h+vXr8Hq9zH2aJUJTb+o1W+wowXLWUR3n\nOng2J+KXvvQETrMBEYXxuOw56XKYYBRkrEQPFky3VX07yokSeA54edCDu8sxBL3qRX4tro50bGjS\nPcmcCI/ViEvdDkyG40jli0gqSstDfjsWNQJDO5Yj5LfjcXhXtU3UvE1GHjrhMxRwYEYzqqPPZcWG\nxt/jsQpYT6jFVp/HqjMvDwf0c78MPKc6/2xBwt2FCG6HvHh5yIe1WLrimRoKOFTDWsvsphjNFgNO\nzG9pXrMkI5UrYPRCAA+WdlQl/qxJ9QJ30GG6TCZfxF4mDyujZ1PAaWF2qnZajFiNpfDq1yYxcqEL\n779yvl3s20UMnaadSjqd1v2g1fLRj34UH/3oR1XbPvGJT6j+/alPfQqf+tSnjvXYZqb1r4IW4TxN\n0odx3pEhURQxOTmJjY0NjI+PVxVCQOeJIVmWMTExge3t7ZqlxZS0Ugfqf/t3T7Ecy6DPrTYfbyZy\ncFoMsBh52I1q8aOtstpJ5XG9z4m7yzE4zYLKP9TtMKlMzB6rARuKSe4OkwCXxYCsKOLuUhTZgqTz\n5vg1Zftmgz6aw5okv7GnFi9Br0WXNnOY9LdW1lrF+rrwjM+CNfdruEvfjRoomcjvLe4gkshiZNgP\nv8OsarZYxihwOjEIlIzPLPYyedxd2Ma1fg/s+89nrDIeJBRwMhtBBpwWJLJ5dLvUi3C/lz0fa9Dv\nAORSL6pPfeG7VaNKp6WdxNBJI0OpVIrmkilo/augBThvk/RhnKcg2dvbU6V+jEbjoft3khhKJpNI\np9Nwu924detWXarFmiEdeBw+/84Kvv60NBjVrEjDuK0GxNIF9LlMWIllYNZECDYU88kGPBYYeQ6T\n4VI0ZFDjH+rT+FQG9g3MPAeMhDzo91jwzkK00lOIA3RdpbUNDFleIO0k+X6PVVe+73fqf13vJfVR\njgjDmB1J683TOwxvT54hLFhG5B6XpTK9XpRk3F2IIJHJw2426ITdcMChE6AAmJVeyjTd5GoUAacZ\nAYcZfW4zs++QjzFeBACsRgGRRBYWI69KmZoZ6ToAqqaN0WQOv/Rn32Ge32lpFzF0mteRyWRoFIeC\n1r8KmphamaQP4zwiQ7IsY2lpCY8fP8atW7eOXRHVKWKoXC1ms9kwMDBQt75KtTzOeQmtx+E9fPYb\n85V/JxSjFQY8Fjzfba/MJFMKDa/NiM19sRD0WDDotmBJYSLWTqrXGpatxlKV2aDXirtLsUrkokzI\nZ0NKM7BVW2nm0lQzlTxF6khRD6M8nRWdiWTV2ywG/fwwr9WInbR+rhprztgqw0+TZxiO+xiG6JxY\nxN35CJxmA15U+H48NrZgYU2vHwqoR34sRZKQJAkBG/sHEqsRJACk8qXrYXkniT6PrWKyLk+w15LW\ndMy+O7+Nf//6Q+a+p6FdxNBpJ9aTGDqg9a+CJqWWJunDOKsgyefzuH//PtLpdKV3UL2O3eyUq8XK\naTGDwVD3SE0zR4ZSORGvfnupEl3hIKv6AHmsRkzsR3o4AMuKtFfQUxIZzwVsSGQLEDWvU9vUL66Y\nDu8y8xD4kmF7cT/6o32fAppIhc9u0vUg0lYzhXx2ZDQRGda3WDtuo89jUZ0fAFzsckH7yXnN+s9y\nKHDQgLHyfG6rrq8R67gAmCMsQn4HEtkCtvayeLi0g2v9bgR9dqaY8jvYFWNeO6PXUjqPjFisVIkp\nYaWzOABL2wdjTqbX47jW7ykNuI0kdPsD+ko+APjjt57g7el15v4npV3E0GleB4khNWSgPmfqYZI+\nDEEQkM2eri/Hzs4Onj59isuXL1faqp+EdhZDrNli9e5v1OzVZL/+D7NIKnw5Qa+1Uir/csiNmCK9\nNOi1YllRRm828rjW68BipDSTTC0mZFXJvYE/GL76Qp8dCztJPFpVG343NSkpbaRiwGvVVWxpGzb6\nHSYs7pT+n+dKKTKzgcfIsBccOBQlGQInI5LKw2E2QCxKyIsyBtxW5PJFWIw8jAYBJoFDj9MM67AP\nHFea+ZXMifCYOczH1efNF/X9enrdFl20ps9jZUZwIox5ZF1Oi8rMPLUWh4HnEPLZYBA4VZor6LNj\nh/EcrHQaAIR3c8jkM3hh0IeJldJcM5fViHBMf26DPgeWd9Qm8IfLO3jf5V68Pbuh27/XbcNGXC/4\nBJ7H//TF7+Gv/9VH4XeyG0kel1r052kE5Bk6OySGzhFZlhGNRmGxWCAIQkO+ZKcRJOXeQXt7exgZ\nGYHFcrobTLuKoWrVYvXufN3MnqE3Hm/hK482ca33IJIYsJuwEs3gep8DD5bjKv+H325SiSGbkcd7\ny0mIkgwDD1WKLOixYVWx8A/57IinC+hzmzER3kO/04A1hanZbTXoZoJp54+ZNWm2PrdF1ck55LPB\naTHg5ZAXu5kC1qJp7KbyWIulofwIXgp5sbCtjl4M+22qgatAyRT9dF0tfC74rfBYeAwGnLAYDEjn\nRRV6bJsAACAASURBVEiSPlojMdLefW69GHKaDczyeVaPnoDTgrdnN3GhywlJPiilZ40ZAYC1mF6U\nlLpul97XJ6tRvDTkx4OlHQz6Hdhdjer3d5uxvKN/7pxYxOiFLtxd2FZt7/VYmWIo5HdgfnMXv/rF\n7+H3//kPMM/3uLRLB+rTltaTGDqg9a+CJqFYLCKXy2FqaqpilG4EJ/UMpdNp3LlzB0ajEaOjo6cW\nQkBtPS3H4byFgjYtpq0Wq7c4adbZZOF4Fr/296UW/CuK1BeHUqXV0k4GfW4L9hQeIeXp3g66cHcp\nXkmvDfvtqhlmXU61UbjfbUZeFCvmardZvQgM+tShf6/NqBNDWhN00GvFy0Ne3B70wGszYjmawpO1\nXdxfimFuK4msKGEo4MBx3iJtib/AA4uaNJDFyGMlmkE8U8TEShx3FiKYCsexuJPCc90OjF3w43KP\nEwLPYWuPUUHF+LhDAYcuxQaAGaXp229IubCdwFo0ibELAQg8V3WMByvi1KMYU1KUZby3tIPRCwFm\nBR6Aqu+dLMt4sF+lpsRQRZiVzdnffLKGL3xnmv2kx+Q0JenNyGleBxmo1bT+VdBgyibpfL50EzEY\nDA0ZSVHmJNGZcDiMBw8e4MqVK7h48WLDxcxZOG9homyiWK1arJ3SZKelKMn411+eQiIrYsBjUfXx\nyRaKpZRQvqib77WzP3Ps9qAb8XQOaYW52aMx5ZYvS5tJwO2gG3tZEQnFcbQpMIumMimoMRUb9xsi\ndjnNGB324mLADkmScX8pivdWYoil86UxFZpUm4UxdFTbD8hrNWJNIz6GA85KVVuZCwGHrnJtOOBA\nOl/E3FYCdxYimN3cg99uQq/HgZtBDwSFH2h1W98ziCVCAg4zNvf0HiBl+b4oybizsI1LPU7muBCW\nKVv7HAAgQ8bdhW3YTOyEQ4RxHgCwvZdGUZaxGk2iX3Gs3SqT7ZWRrt/+yn3Mbe4y9zsOnRwZojSZ\nmta/ChoIyyRd76nxWo4TGRJFEY8ePcL29jZeeeUVeDx6A2SrcZ7C5LizxRoRGarlc5/mtfzx28u4\nv1JajLoU/WnMAiDKMtb3e/8oF06rkcdKLIPbQRcerezCrzHnaifbR5I5DPtt8FoNeG8lrupoDQDb\nKbW5OqEph1eWbdtNAsaHvRj22bCdyOLuQhTz20mdmbqfMWJCO3/LZzPp0nGDfr1w8Nr1FVesvj+s\n/j7dLgseLEcxuRqDwyJgZNiHmwMeRNL67/hWTG9CHqjSv2eLJUxkIJrM6jpNV0udaT1XQMlbdXd+\nC2MXu1TbHWYDVhhmaJfVWDGCJzIFGHgOdrMBBoFXma2VKOejZQtF/PKffYdpBj8O7WKgPm1kiMTQ\nAa1/FTQAWZYhiiJyuVzly1ReqBo1rLTMUZGh3d1dvPvuu/D7/XXrj1MPzsO/c1RarBbHPCnNFBma\n2kjg7yYOjK9KwTM27MX05oHfQ1kNFfJacWvAhUere5AgQ9K8JqXAsBl5dDvNWIumsRbPottpRkQx\nyd5nMyCaOfi+CTywqClN380UMOS3YWTIA0mWkBMlzG4lUS7vcluNWNVEc7QpGpPAYUEzQyzo0wsf\nk0H/65wVbUkyhrPmCvpryaKI9uymC7i3uANAxoDPhpFhPyz7vZoEHthI6M3XMsOQ7bKWujqztidz\nIh4tRzF6IVBpXxBN6VNkdrPelwWUmi2mciLuzG1h9EKXYjs7xRjyO6Ess1veSeJClxPDASfyDNO2\ny2pCWFNFN7UWw2dfe0//5MegncQQldafjda/CuqMLMvI5/OqTtJK6jU1vhrVji/LMhYWFjA1NYUX\nX3yxrv1x6sFZI0PHSYtpaSbPUL2fu1CU8Guvz6qqvMo+nJeCLmQVaS+LgVN5ibqcpooQAtST5AN2\nE7b3xY7ZwGNkyIO7i7HKMNV+j9rT1qdJvw377ZW+PxyAFwZc4DkZSzsp3FuKIVOQdJ2RQwxRs62J\nFLEaFLIiJtGkNloi63oVCTx0pmtAZnZyjjOiL2ajgOVICncXIjAKHEYv+PFC0Mfsd8QqyR/02ZnC\nJKNoX3B3IYLhgBNBn103VgMAhvxsf5KyhcHdhS2MXAgAgK7vUxkrI6U2uRLFgJe9SIf87FYfX3pn\nDu8+01ekHUW7iKHTltZTZOiA1r8K6ogyGlStZL7RYogVGcrlcrh37x5yuRzGx8fb8gtwlijNcdNi\nrGO2ixg6Kb/3rSUURKkygd4kcFiOZjDss+JJeA85hXAI+Q4GsN7sc2I3LVaEkNMiIKyYMda/P3+s\ny2FCv9uMjKZRoqD5bAyavjoemxEcgFtBN0I+G7J5CdObysVcL07MGi+Q02LAiiZSpJ2bBkBXMWY1\n8rrnHvTZdem1C4xRFYM+O3Y1+1mMPHNchnIW2F6mgDvzERh44OUhP3oV6T2bSaikKZUU8/qIDgdZ\nNwj22eYePFYjLve6dftXEzeqFKcM3FvYxshwAGlGJAwAUlWaLSYyedwK+XXbq5mzg347fvUv3kY6\np4+EHUa7iKHTRobacS04La1/FdQB5Vwx4PBO0o0WQ9rjb29v4+7duxgaGsLVq1fr8sVvxIJ9mrL+\nk6bFWMdsFzF0kueeWNvDn7y9DKeiVH7IZ4XVyCNXKCJXlLEWP1iEXfv7Pd9tx+xmQhUlCnnVYzZM\nAo/L3XaIRQkLkbRuovuOJtKhrArjUPKmBL1WPFrZxdJOWmfGDvlsOk9RXFNBNcSInKQ1osxmErCs\nSddcCDh0Iz60xnGAPUaji9HZ+kLAqRt1YTHyzOn12UIR9xcjiOxlMDLsR7fLgmHG+QCAyDPGeDiM\nqm7hZawmA2bX4xgZDqi2a+e8lQlr028y8GBxmylieI7DUpVmi+uxFOY24jrPk7b5Zhm7yYjVnSQ+\n83f3mX+vRruIIWq6eHZa/yqoMeW02HE7STdaDJVFgSRJePr0KZaWljA6Ooqurq6jH3wONCp6cVIx\ndJq0mJZO7DOUEyX8m7+bRlFWd2x2WYwI+axY38uhy2FSiZZ8UcKwz4pwLAOfw6QSMDbNfDKrkcfC\ndgqxdKEUrVDME7Ptl6OXMQscVvdF1+VuBy522TG5uqvaR7t4djnUosNi4LGo8QJZNOfEMaJJQ367\nTmiwoiWsXoW5gn5BZ/UCUvZlKnMh4NRVoXGQsbSfdhMlGfcWIogmsuhzW+G2aofRssVUv5/9Q2Av\nk91/zm2M7pffcwBTxHS7LExjdtDnwHsLEVwfUA95HvTbmaLKazdjPZ5GKifCwHOVz4PjULVTdWZ/\nzMdffHca32c0cKxGu4ih00SGyECtpvWvghqjNEYfJ33SDGJIFEW8++67MJvNGBkZgdnMnkFUCxpV\nTXcSoXDatNhZjnkeNEM12efeWsB8pCRQworePRYjj8fh0kKlnVSfFyXsZgpI5ou62V5KI/H4sAfv\nzMcqi33IZ1NFZIb8dlUZ/VDADq/NiCsBE2a3EkjnRZUI4yBXOlWXKWquzeGAfjirNl0V8jt0hmeW\n8GFFVvQ9fvTCCoCuHB8oVVdpsTMEUijgxJ7m2KIkYy2WgixLFREDVB/OyvL/KEUWUJoL9nyPE8/3\nuZkiptrk+S6XBaIkY2FrD8/1HIiuAGPALbA/qX6fpUiiIqL6vXbme1Lar9RzSpaBf/PFt5E6Zrqs\nXcTQaUvrTzJuqd1p/augDpxkEWqkGJJlGWtra8hkMrh27RouXLhQd5N0o6rpjhMZOmtaTEuneYYe\nre7i8++sAigZnXdSpQXnao8dz7YPFnhlJVav04R4Oo/Y/ngNZeNnDjKWomkYeA4vDXoQSxdUFUQB\nTbNFpQAxG3j0uSyIp/OYjpSiQ70aoRXy2XUpMW1Zvjb6YhI4nU9Hex5mA4+iJKPfY8WQ347nuhy4\n0usEz3G4EHCg32OF32HGoNeKLU2zQpaHqMdlqXRyLmPg9ecB6Mv7gVInaC1GgcPCdgJ7WRF3F7YR\n9Npwrd8NFyNFB7AHwV7sdiGrMWVPhXchFDLwMDxUWv9WGXlfaWXyRewkspXUV7Vr2aypyLu/sI2R\nC13ocbHF04BGJK3uJPGZr9xj7qulXcQQldafnda/CpqMRomhcu+gaDQKu90Ot1tveqwHjRrJcZR/\n5zzSYloaIU5q6Rk6jEJRwuffWatEEPo9pQXYbTUgVyhic09p6i0JEKuRx3Nddmwo/qYsiw/5bJBk\nGVd6HXiwEodbMzVem4Yqp7ye73HAbzdiO5mtVJkB+qbMAadaJHQ5TdjWNFLUGntLkRMZbqsRV3td\nGB32wW4ScL3PhZDPCqdZQFGS8Hg1hnAsjaVIEnNbCUiShCfhOBYiCYTjaewkswg4zbAYOAQ9Vlzv\nc2NkyIfLPU7cDHpUVVf9jMqpC10OncnaKHBYZPTeYUV6LnY5VdVlSztJTIXjsJkEnWepp0qHadZw\nVgAwWu0wGgR0afonbTJGZwBAWDE2JJ7KQyxK8Dss2GIMcwWA3bTe9P1oaRtWI/s728PoCfXFt2fw\n/Zmjh7m2ixgiz9DZaY8mMzXmJIteI8RQPB7H48ePceHCBfT39+Ptt9+u6/GVNEoMHebfKc8We+GF\nF+B0Os/tmM1koD6PCOBhr+WPvrusGjNhEkrekaDbst9fqBRxKc8V4zngUsCuWtBt+80Wy3Q5TDDy\nqKTXtFPj1xVVZhyA7UQOL4c8uL8cA2RZl87a1FROaVNiAx4bthX78FypJxHPlVJwfocZDrOAnUQW\nO6k8djMl4ea1GVUl6ld6nJjeUA8cdTMiLhwHZAtSqYfRfhrsxZAHk6sxACVjebfDBK/NiKt9bsxt\nJSrCxmPVP99wlxMz6/puy6ySfFYESODw/7P3psGR7WeZ5+/kvu+Z2pVaqlR1b+0lqYwBux0TMIBn\npht/mAmC+QQxQziMp2eaJro/MA0xBETDBAFNY5Z20z2mewLM4HFjgxfMeAHse31VUqlUi2qRlJJS\nSkmZUu77eubDyUzlWXRvla6qdOtePREO38o8eU6e1Mnzf/J9n/d5uL22j8mg49qoj6WolB824LVp\nJtUfZWS4nSpykK/gtOgJ++1sJotYjTqVVxOA32FmT5GhFs+WuTDgZlvDhNGg17Gxn1M9Xm+KlKo1\n7GaDqkWn06hIiSL8/t/c49pYUHN8v4P3S1DrcZy0m80mRqPaEPSDilefEr/H8DLJkCiKRCIRnjx5\nwo0bNxgcHHwpx307nGZlSHlcZVvsJIkQvL8E1G+378hBiT/+XlQ2pp2rNLg56ubhbkHm8Bz22ag1\nRW6MuLm/k5Olz4f9tm5lyW83IYqwun+4UPYGtwbsJlny/LVhN6IIC5tpRBFG/XaZjsdrM6paYNtp\n+b97W3Rem5EfmPBzLujAbjKwvl9kfj1FIleR6Y6GvVaVV4/Lql5AtEbHtXRAWz16oVylwepBiUc7\nGR7vZNALIq8PupkZ96O1PivF0NL7s5HW8BIqaOiXxoNOSrUGmVKNpc0k10Z9eO0mlV1BB1pi5X6P\ntVtFyleaxLMlXhv0MBZ0aeqOvGbtfRsNOsaDTlnECEA44KCm4ZdkMxlY2kwyNaB2y0/mtWM+QOTf\nfnXxiOfaW4jic2ttzvD+xBkZOmG8LDJUqVSYn5+n0WgwOzurKneelrbkvdImexFtMSU+CJohURT5\nP77yBIfZQCIvLbp6Qap6LLVjOHrFux6bkelRNwubGcx6QZY+34mgCDpMmPWCjLwMuS2ySs+QV2p9\nGPUCM2EvegH2e3x9AoroCmU4a5/TzIHCB6hcazId9nKx30m2XKfWaHFvO9vVFUlmiPJWT0hj5F0p\nlNYyUQw5zcQV4bDDPpuKWHltBnbbn0Ol3mI5lmFx/YAH22nCfjsz44feQVqiZS0djUEnBbAq4VG0\nvZY2k7RaoqbWZ9hnU1kOAAy45RqTcr3Fyl6GkEarCsDjOuIHSKPOg60U18PykX2fXTsoOhx00moH\nut4YO5yMtRj1RI+I7ShXm/zJ3z1ieTup/R7gVEO1TxOnPZX6XsQZGXoGvNcE1IlEgoWFBSYmJpia\nmlKVR0+LkJzmsXurNLFYjHv37nH58uV3NS32Tngvtcle1L7/4s4ud7ZyDHkOF9IRr5VcqU6jJRGj\nzVRvfIaexahEksJ+m2xSq1hr0uc0oxckX5xeLZHSj8egFxjyWBn2WGUO1B0o/XeMiu/AYDuVXS8I\nXBlyc3PEw+O9HAubKR7v5WiJokqTMxFwUFY8ptQtaQmbJ4Lq12k5KCsF3gCDGj5EY0Ep0mLjoMDt\nyAG7mRLnQk6cFgM2hV+PMsoEYDykNnUEqGh49OiAubUEM+MBTD0VvqPEylpfpXpTZD9b4npYbZKY\nKqi1SACldvTIQiTBxdDhZ3VUa87Royd7Ekt1J9dGA05VUG8Hm8kczZbIv/r8m6qWaQfvl6DW4+KD\nSASPwgf3KnhBeJFkqNlssry8zPb2NrOzs/j96psPfDDJUGeK7f79+xwcHLyQtpgS76fRei0k8lV+\n51sRQJ65NeK1sJuTqgZhn60r1B3xWnmaKHQXaJdiUqtcbyKKInu5KsNe7cW2A5tRT7JQZb09xq9s\neSn1KWlFFcNi1DET9uKzGbm/naHRbMmIgwCqEXe3Td2G2lJMWU0EHaoEereGvkcLWkJnLXjt6v2J\niLy1to+AyMx4gGGfRAa0psA8NjXB0gna1aJOZth8ZJ8hj6076aVFskDDVBGJIK7Fc9zfTMoIkdWk\n1/QjMul1bPVUDFcSJab6pO/qRjytedxSTzWuVGtgNeox6HWafzOAIZ+dXPuaeLCV5D///WPN7d4v\nAurnhSiKZ0RIgQ/eVfCC8aLIUKftY7fbuXHjBibT0Tfg0xzvPy0yVK/XWVlZwePxvLQA2vdbUKty\n3//nN9YoVKXrqNNKujrklI2rdxLZnWY9NpMgq/ZUen7lj/tt5Mv1bg5ZbxUCINEWZ5v0OmbCHt5c\nS3ZJR7/bLNPxDCj+bTHAZps0DXut3Bj1sJUqMr+R6rbWTIrIjbGAeuxe6TI96LGSLMhJlpZuR8sV\neSej1gtp+QvF8+pWlJb+yNsWRBdrTebX99lOFZge92k6V2u9n7F2gKoShh4isL6fJ1UocyPsZ1eD\n9Pgckhmiat9BqRLVFEUZIRoPOjUdsMeCThkxbIoiO+kSl4d9ZCvq+5YAbCTkwvG1eJYb4YBmCC5A\nyCWvzP3uVxfZ0RBsw6tfHTmOCLxSqWCxaLckP6g4I0MnjJMmIqIosrW11W37hMPhd7zwP2iVoVgs\nxu7uLkNDQy+0LabE+0kzpPzM/mElyd+vSloLHRBNl/HZjGymSjLC02y10Akw4rNiVghRO5NjQYeJ\nfpc8bb5XO+OxGohlKgQdJoa9ForVhqy9NqBY8JXtpkGniRGflWsjbmLpEpsHRVUlSTlS71foZ/QC\nqvaXVltLab74rHqhEb9agxOwG2WfSWd/EY0KjlbKvdiC5Viac31OLg9LxoQ6Ac3xe7+GFxFAIicn\nN+Vak1iqwJDPrtISjfi0PWl6R/B7CZHdrF210Zq8K1QbmA06TXH6kM9Osaa+p96OxDX3D+oJs1K1\nwa9+4a0jt3+VcZzqVrFYPBurV+CMDD0DnmdxPckFq16vc/fuXbLZLB/60Ieeue3zQakM9bbFxsbG\n3rZa9iLwXtIM7ezs8OTJE+LxOLWadvjls6LaaPGf5rYptyszoz4rlXqLAbcZAWRkaDdX5caIm4e7\neZnZ4qDbTLbcwGszYtQJMk2NxaCTTY6NeG1M9TlotFpEDopdofXhiSv+2fPvQZcZn1XPRrLI0lYG\nEYmY9cJpMahyxJRj/OMBh6oypNSiGHSCivg8q14o5FQTqz6n+nqdDLpU4bTScdUEp9PKWo3neLCd\nYjLk4MPnQpoVoLJGBIjXZpJNtx2+fzvzkX0m+1wyT6Lev69s34pKVFMUubeZxKjXvm92ojOUEATJ\nfVqnuN/2ubUXbZ/VwOZeCqtR/b60Jsy+/XCbv7m7obmvVxnHDWk9I0NynJGhE8ZJVSXS6TRzc3MM\nDAxw+fLl57rYPwiVoU7bsLct9rInJN4Lo/Ud+4BkMklfXx+lUokHDx4wPz/P6uoqyWTymYhx777/\nwxtRmRO0z27k5oiLh7t5hj2HRMNnM9LnNDMfzQBy3U6fy4zTYsBpNrCTrbKXPSRQYwphtddmYC1R\n6LpUK12We/2NQPITkqbWvOzlquwX5YuxsqIx5lcHr/ZmngF47OqKxLYiymMiaFcJk7X0Qlp3gIaG\nXkjrctXSwEweIYhW+gutJfLUGk0uDrgYDx7GLAiIbOyrW0ThwFFRDNIbe7yTwWTQMdbebj+nFkNL\n+1YTNQGR+9Ekl4a9imdENo+Y/jrIl3m4nWJ6Qp6jeNTXOhzykKk0Od8vN5g1G3RHHuOLc2vPHNXx\nquAssf5kcEaG3mMQRZHV1VVWVla4efMm/f39z72P93tlSGta7DQI4Gm3yUqlErdv38blcnH58mU8\nHg/j4+PcvHmT69ev4/F4SKVS3Llzh8XFRTY2Nsjlcm/7nrfSZf7jm1uIPR+l2aDj0Z60uFh6foWP\n+Cw8ibcfNwiyao9RLxBymImmpPZaL6HppN0LwEzYw06m3K3CGHSw0UNUvDYjOz3mi16bgUG3hXq9\nycJmCoMOYjl5JSyuWLSVeqGwz6YiXMpqzIDHohrNd9tM2NsOziGXhWGvDb1OoM9lwWMzYTXq0Qla\n/kLaeWTxvNppWSvfTKt1NOKzkSqoX1+sNni8k2Vjv8DNMT8+u5mxgFPTd0jp8dNBr0g6ni2zlykx\nMx4gmlQTjHDAoe1pFHKRr9SJxLMysjLqd2qeo8Ni7Oag3V6Lc3X0UIgdP8KpuvP+l6IprvRsP+K3\nHykAX9lJ8wdfX9J87lXFcdpk5XIZq/Xthxg+aDhzoH4PoVwuc//+fXw+HzMzM8eecjjtylCjoS7J\nnwQ603StVotbt27JRNIvu2UFp0uG9vf3efr0KZcuXcLj8aj+3gaDgUAgQCAg+bhUq1XS6TTb29vk\n83lsNhs+nw+v14vNZuvu+1//zSrVRqu7UOsEqeLTaZl1ojZsJj1Wo66bXTXqs/E0Li2iJr1Aqdpk\nre3ZM+yzkuqpGhVrTUx6Ha/1O3iwnZFVicYDDlbih1WMEZ+t+9rXBpx4LAbejBz6xoS9VlYOesiT\n1ajSCylJQ9BpkVWGdD16oZDTTMhlIeAw0++yUKu3KFTrpIs1CpU6xVoD2m0hg07gIF+WVW36XRaK\n1Tphvw2nxYjJqMdm0pMr17Ga9Oxly4giDLitKjGyUS8QSagJhzKEFSDksqpaXAYdRBKdwFKRO+sH\n2Ex6boS9bCULqkDahEalJ+SysKcgH+V6k0q9wfR4kPnIvuw5v8OiWXXq6IjK9SbxTJFwwMnmQZ6g\ny0L0QO0wPRZ08mDr8O+6Fs9IWqFKndgRwuf9nlbY9kEet81EtlTD67AC6mPYTTpiqQKf+/ZD/utL\n/VyZOH2T2pPAcSpDhULhrDKkwBkZega8DEHu3t4ea2trvPbaa/h8vne1r9MmQy+CIBQKBe7fv8/w\n8DDDw8Oqv8kHpTLUarVYWVkhm80yOzsr00m93XVqNpvp7++nv78fURQplUqkUilWV1epVCrYbDbe\niBb4h7UabqvU2gKYGXUztym1wXo9hc6HbDLxr6vtAyMAV4dcLLRfA2DsqUAIQLJYY8xvZWk7y8V+\nJ497oi3cinF8g17AYzUyHrCxGM0wHZY7ENvN8kVgxG+TteucZr2qKtNxOHaYDYwFpOT7eK5MLF0i\nnqsQz1W4PuLhbvRwzNukQVQmQ06eKOIxBn027mwkyffodmbG/NxrR1/YTHqGfXaGvDbcJtjJ1ci1\np9omgk4eK/ZnNug0CZJmHlnIpYrrKNWaxLMVRnx2BN3hOXhsJrY0YjyGfHbNSozFaOB2JMHsRIj5\n9f1u60rLLRrkGqVcpY7BoGfAYzvyO6qMzChWG/gdMNHn5k4kodrebjbIWmGpYpXrY0GWNg80W4oA\n431eHkQPaLREfv2Lc/zix4Ypl8tEo1G8Xi8Oh+OVnCw7yyU7GZy1yV4AnkdL0mw2efjwIbu7u9y6\ndetdEyF4/7XJnsVE8TTG3F92NarRaLCzswPA9PT0sQXjgiBgt9sZGRnh6tWrzMzM4PIF+LPHEonw\nGaXPMeQwyoTGYb/kKXRzxMXybp6NHk1NR0Q8PeqmUm/R+6n0VoUmgjYMAjxtV38cCjJTVnj4WA06\nWmKLxbYuKaFoLXVG/ztQmi+GA45uTIROgAt9DmwmPRN+O6VqgwfbGcq1Jk/28j37Etk8UPgLheTB\np3BIAHvR0hglr/QQg1KtydO9HKlClUfxIrlynbDfzvSYnwGPFaNCpDwRcmoQH22djpZ+SS/AeiLH\n+n6ejUSe2fEAFqP+aL3QEddzpwpzO5Lg2qi/+z61ctEE1BNtkvmiSFbD1RogpxHOGk0Wui1VJcJB\nl+q7d3dDcqfe1vA2ArD1CPOXtnMc6APYbDYMBgPRaJS5uTkePHhALBajVCq9Mi7Nx6kMlctlHI6j\nNGMfTJyRoReAZyUj+Xyet956C5fLxfXr108sNK9jQHgaOEki9jwmiqfVJntZBCybzbK2tobb7eb8\n+fMn+gtWp9Px9dUSyXbXxOdyIAA2Q4tK6ZAUuEw6xvxW7u/kGPPbqHdcoEUpV2x61MN8NCPTFVmN\nOqJJaSEd8lgIOczEejRAvSPjkhGiRLDcViM3R928sXbQbc15bEaZWZ9JL7CpGqGXt36sRh2vDbiY\nDntxW41U6i2+v3ZA5ODQHLKomIYK++wqE0etRVkdVyGqxvP1OjQqO4fbiUgtuvn1A2LpImaDwI2w\njyvDXkwGnXqyDhgPOFWaJ4BcWU00JkKu7nRZSxS5HdnHazPhOsIoMqbhL+S2mWTmiXc3DzjX52LY\nZdQkN2MhbY1SSxQRBClCoxcmg45IQh1AC7CTKqoE1SBVhrSQLJSP/G7kFZ/Pb35pnnpLYHBwFJyb\n1wAAIABJREFUkEuXLnHr1i3Gx8cRRZG1tTVu377N8vIyu7u7VCraTtrvBZxVhk4GZ2ToGfC8C887\nEQJRFNnc3OTBgwdcuXLlxL1x9Hr9Kz9N1pkW83q9z2SieBqVoZfRJhNFkWg0yvLyMhMTEy/kBrab\nrfC99cO2VrHe4saIi41MA9F4KLKsVqvkimVqTRGz7vD6HvZaGPfbpDR5kGWMhf02mqLImN9GsdaQ\n+cXoBVjvqcCE/TYK1QaXBl3oBJFqoyUL/xxV5I+NBxyHhAxwWw1stcXLI14r02EvmWKVRztZFjZS\npIs1gk65346WTkfLyFCZKWYz6VXj7uGAQ0WQJkMu1cj+mMZ2dpOeSCJPodpgcTPJ/e0URp1EHM71\nuWTb+p1qzyCLQcdaQq2T8Wh4+uxmSqwnssxMBGWTd/1uq2Z6/VjQqSoYPdpJ47bqNffv17ARAGlk\nfy2eZWrALRufHw+6ZH/H7jkZ9UQSWe5HDwgH5D+EChXtCpPfYWFYo+ql1wkq48a9TIkvPTjUQHUq\npsPDw1y5coXZ2VmGh4ep1Wo8fvyYubk5Hj9+TCKReNf2FSeJs9H6k8EZGXoBeDsyVKvVWFxcpFgs\nvrDIiFe9TdbbFtPSBx113PebgLpTGcvlcty6dQuLxfK2xzvue/ntb613nZB1SHqNJ/G8KnfMbLWS\nrEjH6G0ZuQ1NHu3mEJGqNb3TYA6znsmgnWShQqZUl1V2xgN22X4CDjPTYQ8PdrKkSnXMCpdqpW+N\nsloT9tu5NuJhqs/BVrrE03iONYW4Vzk1NhF0dEXgHSg1Jw6zXjOPTClIDmoYG7o1WmkBDbIwEXKp\n9qfTCbyxEmd1L8uY387MeAC72UBFw4Bwss+lymsD7em0gNPMVqrI7UiCcMDBgEdaFAc1/JFA/bl3\nUK23cFmN+BTnXTtCs9MZ2b8XTTI9fhjQ6tIgVABjQekzqTZaNMVWt6IkERs18QPpO7m0sc9VRQDs\naMCp+tsD/PX9BBtx7aqUIAi4XC7C4TDXr19nZmaG/v5+isUiDx484Pbt26ysrHBwcPDChkaeBa1W\n61hk6KxNJscZGXoBOIqMJJNJbt++zdDQEK+//vpzX8DPitMWUB/32O8mW+w0zvlFErBiscjc3Bw+\nn6/rM/VO5Os41cU7W1neiKS6gukRrxWXxUCx1upqhABmRl0sbnUWDZF4Qbq+Q04TBqOxG6Qasgqy\nX/kWg47dTIl8tcmQ29L1EgKp7dXBkMdCq9VifvNQtKysxihdpDsiZZtRx+yYD4tBx91omqftcf/x\ngF1WWdILqCafnIqxdUljI99GK1ZC2eoBVOaLAFmN1pWWKaJZwziw97gbBwXmI/voxBZ2s4GQonql\nFCBDR3ytJg0j/sNFcDWRI1OqcGPMf+S1ldCoFoHIXr5GNFnAajL0EDxRM48M5CP7tyMJZiZCgNq0\nsQNnD5HcShZ4re1ZNBpwakaOAOy3xd+xVEEW7up3aFerGi2Rz3xtUfM5JXQ6ncy+4ubNm/j9frLZ\nLHfv3mVhYYG1tTVSqdRL/THabDbPRutPAGdk6AVASYZarRZPnz4lEokwPT1NX1/fSz3+y8RxSUmh\nUOCtt9565raYEu+nNlk8HmdpaYlLly4xPDz8TMc7DhESRZHf/MYawx5LV/Dc7zLxcFdazLxtsjLo\nNsvaJMMeK9lKA6tRh82oJ144XJj6vIcEdsQpML+R6iaUKxfwDnm4OuQmU6yy1tMyU06BeWzGbgsM\npGpFtlTn+pCTVqvF7fUkuxn5oq0SIwedqlgHZbtqPOhQaYiUFSpQGxBqxWjY2q0v+XvSHp/f0yAc\nyvcPMOC189ZqglS+ws0xf9ftWisdfjLk0pz2Ul5BpVqTOxsHmI16zAY5yfPZzZoi6XDASaEm7TuW\nKmAy6Ai5rIQDLk0dUchlYU9hJXBnPcHVUb+qfdVBQWGOeGddEkgfRWxcVlPXCymZL3Nx8NDw8Sjf\noYDDxF8tRHjzyY7m828HvV6Pz+djcnKSmZkZrl69isvl4uDgoOvttb6+TjabfaH3puO0yYrF4lll\nSIEzMvQMeDeaoY4xnl6vZ2Zm5qWE471qlaFOW+zKlSvP3BY7ieO+W5w0AWu1Wjx58oRYLMbs7Cwu\nl0u1zUmSr7+8F2d5r4DNJN1IbQZkVZ16U8SgE7AYdLIFNOQ0IQDngw7ylYY8nLVNfM6H7Djsdio9\n+8vlDqsUAiJbqRIzYQ/3Yhl8DjOZUq/WyK7SC3VO3WMz8uFxP8lChbvbOSoNEZ/dJCNLoCYYHoW7\ns6T7kS/0Xo2WjdLE0Wszqcb1J0PqGA2tVtpkyKVqwwWdZs30ea2E+E6uV6Ml+QjtpEvMjPk1W2T2\nIyaxohqVm2GfnTdX4gz57IRchxWD0SOmzoJOeVVhJ11EEESG/dqttmGfej8tUaRUrRFwqSsUBp3A\nukb76tFOEkFF5ySEg/JK8nwkzsUhiRDFNQJmQSJDAP/6i29pTgI+D4xGI8FgkKmpKWZnZ7l06RI2\nm43d3V3m5+dZWloiGo2Sz+dP9Ht8JqA+GZyRoReADhna3d1lcXGRqakpJicnX5qHxatCht5NW0yJ\nl+35AyfbJqtWq8zPz2MwGLhx44bmZOFJXj/FaoN/++2N9n9Li/OwQ89OT8DoTqbC9WEXkYOSLL1d\nBKZHPdyL5Rj2Hi5kArCZKjEZtLGTKak8gHLNw3Pqt+vxGFvMb6RBlPRCvdDSC5kNOmbCXur1FuV6\nU0bclOJqv91ETDFpppzAGtcgK0qNjc9uYktBVMJ+tVmdlku0xagmIw4NgqIVgCqZMqqrRUoDSVEU\nqTdb7RT7AL6e0NSUhsP1iM9OUsO5ut8t/R0jiRy1ZpOLg5Kfk/4IvVCtoa48x7Nlms0WQQ1yc9SV\n67FbqNQaqum2saBLs+1YrjWpNZuqyBXQ/rzzpRohl/VI48bObp7spPmLN58c8S6PB5PJRF9fHxcv\nXuTWrVtMTU3Jxvjv37/P9vY2xWLxXd1Hjjtaf2a6KMeZ6eIz4nkWW0EQ2NjYwGw2c+vWrRMbmX9W\nvAptso6J4sjICENDQ+96oX+VTRfT6TTLy8tcuHCh6xj9Io8H8O/f2OKgWEOHyGa6zPmgjd10kXzb\nEyfoMOG1GVmIZrCbdER7iIXFoOPNiKTt6V2URn1WBAQSuQrFWku2mIUcpq5H0LDXyqjXwhtrh47D\n2Zx8sUoWDxdsnQBWgx6n2SCRJyCjIDbKtXHUZ5Mt+maDIJtcA3m0SGebvWyFEZ8Nh8WIxajDYzWR\nr9QQRamS0RKlsf/ro14pBkaQFnq7Sc/NMR+1eotSrUGmVFON+YOazIC6bQWSmFnpUO2yGFjX0AAZ\n9AItUWRhfR+rSc/sRJD1/ZxmuGufx0pUgxhUe/5WmWKNfKnG7ESQnYy6OqUT0NQiCcDydhpnW1Td\ne65a+wFJbL2XKfH6sJcnu/WuRsqrIUYH6PfYuLuxz61z/cytylPrc2X1ZxtLF/jIxSESR0R69FYj\nf/crd/hvbk7gOMJ24N3CarVitVoZHBzsGp+m02kikQilUgmn04nX68Xr9T5XB+Estf5kcEaGThi5\nXI6trS18Ph9Xrlw5FUfT0/QZehZSEovF2Nzc5MqVKyc2Tfcq+gx1LBbi8TjT09PveAN8JzIkiuIz\nXW+72TJfWNwFJMF0LFuhUm8RsuvJZ6TrZshjYScjRUeM+mws70kLaNhrYTF62L7odaHud1l4vJcj\nX20iIMoiLwY9VhL5Ghf7ncTSRfJW+a0nWT183zaDwGY7YmPYbcJtNfK9tYNum8xm0qnaW9uqPDA5\nJoNOlncOF/AOibsx6kWvEyhWG1hNOu5spMj0GADeGPWyuJmS7SvgNHHQU3Vxmg2Uag2ZyNrvMJPI\nlpgMOnHbjOh0ApVaU4OgiGxotK20HKbHgy6WoknV472xHOVak9uRBDfDfoY8Npai8veu5c6sRW6a\nomScOOq3E8+UZBW0saCLiEYLayzoZD2RI1euEQ46aTRb5Mp1Ak4zuxotP50gsLEv7Wd5O83MZB/z\nbbfpo0TVg147e+kCC2txzvd7WNmTLCGMeh3rR2iPqo0GowGnqj1oNenZ7WmlJvMV/ugbS/ziP5nV\n3M9JojPG3xnlF0WRQqFAOp3myZMnVKtVXC5Xlxy9ncHqmeniyeCsTXZCEEWRjY0NHj58yOjoKC6X\n69Ss3d+rPkOdtlgymTxxW4FXrTLUaDS4e/cupVKJ2dnZZ/oleFLTZP/prRjZtpFhwGHi+rCLrXQF\nQ8/LzQaBRHvc3taeVLKb9Ay4Ld1RdKdZ39Xp9DnN1BrN7n7DfrvcUFGAGyNuVuKSl85GzwI+6rPK\nKj0TISdWk54bI25i2Sq1WlUm4A775Kn3AbtB5UytJEd2s4HJkIOZcR+vD7oIuEwsbCRZ3Ewxv57k\n0U4WnaqZI7KpGKkf9dtlRAhgPKSeNhv12ynVmqwmcixsJLkdOUCvg1KtwWTIwex4gHMBC+dDTtKK\nqTmdAOsaImutltWwz0Yip26nCYLAUjTJ5WEvfe0W2FEVnckeY8ZejPjtLKzvc2HAIzM59B9Rten1\nF9rczxNyWrGbDZp6IZBE2L2ty/m1ODfHgggCbO5rj8536mhNUaRUrXen6MaOEIsDZIrVri6uF8Ne\nu8o/6U++s8zWEdNwLxKCIOB0OhkdHeXatWvMzMwwMDBAqVTqjvE/ffpUc4z/uJqhszaZHGdk6Bnx\ndgtNtVrlzp07lMtlPvShD2Gz2U6tMgPvzTZZ77TYlStXnnta7J3wKk2T5fN55ubm6Ovr4/XXX3/m\nG9lJtMke7xV4tHe4wJsMOh7EpIUnX5f2fWXQSbxHFN0hNRMBm1yn47e120YGVdp8wC5vDVuNOha3\nMm0DRjv5yuENPajw3fHZpXT4xa0MIuBU/IIVG3IyErLLr6VBj5X9fBWLUc/VYQ/XRzykilVWE3lu\nryd5uJOl32VVLYTKttZYwKEa71dOxIE8e60DJTkCyTeoJYqsJfLcXt9n9aCM06LnYr+LmfFAd98T\nIe1k95iGyLrfrd3q2G63wh5sp8gWK8xMBDjX59YkPR6bNrnpXGsPt1MEndbu36mksQ+AiqKasxrP\nMuyza+p7QNuc8cHWATMTIU2HbUBWYYqlC7zeHrc/6hxMBh3r8SyPd9LcbI/yd6BFkGqNJr/15dua\n+3qZ0Ol0uN1u2Rh/IBAgm82ytLQkG+NvNBpnmqETwFmb7F3i4OCAJ0+eMDU1RTAo2cafpoD5tI+v\nRRpfRFtMidNokx3nmDs7O2xsbBzrszgJMvTb34rIprSK1QaVhohZLxAvtnBbDKQKNXbbE1R6ATZS\nJaZH3SxsZhjvmRayGnVYjDqCdhPlelPmIVRtt3n0gsCtMQ9vrB22a/wOk0y/0xucej5kJ5oqst+j\nN1EKiSuiETgkKZXq4X8b9QKTATsBm4kne1nubWVwW41kFY7Fys8x4DCrJsSCDrPKl0iLCCgF1kdV\ndqIHaq1OodLo+iKBRITCfgfpQlWmeRr02DSny7TaXkNem4w4VRot5iP7/PCFfioNh6rapRXjAaKs\npbexnyPosjIRcmpWlww6gUhc/fiTnQwfPt+HXieoCGK1rv4sa40WOugm0Pci4LSo2m0LkQRXRgNU\njzA9HA+5eRKTrr31eAaX1dQ933JNm3AtridYjMS5MfFiLVCeB50x/k52ZaPRIJPJkEwmyeVy3L9/\nH5/Ph9frxeVyveMPrFqtduxsw/crzipDx0RnDHpjY4OZmZkuEQLpwj1NR9LTJmMdvMi2mBKnMU32\nPNWoVqvF8vIyiUTihX8WR+GNSIo31zPst3U+VwYd3ItJC96Y30ZTlP7fbTN2CVPYb2PUa+VuNIvd\npGOzx0E6X2kwGbCxul+kX1YxEYmmShj1ApcGnJRrCodnxQj6ZqrExX4nVqOOyH5BRkr6nGZ2eybc\nPDYjmzLyIbJfkUTZ1wYdmHUisUSae9sZqg3pJMYCynaIOoh1VGMkvLd6BdKEmzLyYsRnI6EYvZ8I\nOskpKjvhgIMDhXjaYhCIKMhWJJFncz9PulDlyrCXKyNeDDqBAa/2+Pmqhnan4yitRDxTYidVYHZC\nakWBpJvRivEYDzjJFOXvdz9XxmzQaY7bT/S5NI0QQy4rbz7d40ZYni+mE4QjW2HlepMRvwPl76ph\nv3a7bSdVIKkhVgdkU2rpYpXzA9KUnCBoV9oABj0OfutLp18dejsYDAYCgQDnz5/HZrNx+fJlbDYb\ne3t7zzzGf1oyjvcqzsjQMdBxBzaZTExPT2M2y0u0p6nZgdOpkijxotti7wU8KwErl8vcvn0bm83G\ntWvXjv1ZvBvC1xJFfudb67gsemKZCia9gL2nTeC06Jlw61jazmHrcVcO2CWxcFMUCftsXZLUef3D\nHYlMNXve16jPSq0hcj7o4F4si9Bzl9Ehb6eN+KycD9l5vJdjP19lzC8nLkOKiIiw/9BvSK8TuDHk\nxGvVs50qsRTLU6qLJBQSmmJBTjjGAg5VEKvSY8Zi1LGmqO6c61Mn1/dpjJF77epf3CGXuo0z7DGr\nRvtdViORRI6WKHJ/K8X9aAqX1YjLYlTt93y/W7MypBXX4bQYWEvkqDdFbq8luNjvIei0MBl00dAQ\nawc02oEADrORjXi2257qwH3EBFZHLzQfSTA7eVhpCQe1w2YFATYSWR5Ek8woKjOGIxZvu8Uo80bq\nRVlRybsTSTDZ72bErzbg7ECvF5hfi/Ot+1HN59+LMJvNsjH+CxcuYDQa2dra6o7xr6yscPfu3WeS\nUHz961/nwoULnDt3jt/4jd9QPf+d73wHt9vN9evXuX79Or/6q7/afW5sbIwrV650I0xeFZyRoWdE\nh0XHYjGWlpZ47bXXGB8f12TXp6nZeS+gVqu9axPFVwHPQk6SySR37txhamqKsbGxd/VZvBsy9Nf3\nEzyOFxn1WhGBq0NOmf6nJUK8KC2KnZgLnQC1ZotUu/1l6xHR3hrzcCd6GO663TN63+e0MOQ2s7wr\n/fLf66nsdMJYAQbdFkZ9tq7XEKhFwkqSotdJfkPTYS8Bu1TBiqYPKxiTQadMuA2QrstvcxZRToQE\nRNYVraNzIadqosuqEcGh1TbT8vHJayz8Bo1LYSLoRCk3ypdrvLkSp1ipMz0e6BJELVNFo167WjQR\ncsvaVI920lRqdZVeq4NiVbuFlC5UqTZaPI2lOec/fK3W+YG8HXl7VRJIw9HxGKMBZ7c9trAWl7lI\nJ3LaE4Mhl43F9QRXR+W2FJIQW/5ZiIiIongkeQJIto/z21++/a6NGE8LFouFgYEBXn/9dW7dusXE\nxASZTIZf+ZVf4ebNm2QyGT73uc+xubmpem2z2eTnf/7n+drXvsby8jJ/9md/xvLysmq7j3zkI9y9\ne5e7d+/yy7/8y7Lnvv3tb3P37l3m5+df2DmeNM7I0DOiXq9z7969bsvH7XYfue0HlQx12mLNZvPU\nWkEvE29XgRNFkbW1NSKRCDMzM3i9Xs3tngfHJUPVRovP/N0GIGVqBR0mHsRyPR4rIs1Wi2IdmRD6\n5qibSE87qZNGf33YJauQDLjM3RF7t9VAs9lkdV96XdAhb3P5246/V4fdZMp1VRyGUh8U7WnL2c16\nrAYdVqOOhY0U8VxVlQjvVrhMj/ptqvYUBvlCPOA0dM+tA63ssT3F1JbFoGNV0WLy2EyasRzK7QDi\nee3KiBKdClCt2WJhfZ+ddImrIz7Nhfpcn3a1SEtCkq80WN3LMjMexNAT/WHS61jbU79fl8XY1Qs1\nWiJryTI3x4JS+/CIsFNlTtm9zQNeH/Zp6oUAmWFjSxRJZEt47WbctsOoDSUaLel8t5N5WVtsNKAt\nRI/Es1g1xNMgEf7N9t9vZTfDf3lrRXO7VwmdMf7Z2Vm+9KUvMT8/j91uJ51O86lPfYrr16/zcz/3\nczx69AiAubk5zp07x8TEBCaTiZ/6qZ/iS1/60imfxYvHGRl6RmxvbxMIBJ4pN+uDSIYKhQJzc3Nd\nw7D3Y1tMiaPISb1e586dOzQaDc026kkf753wt4/32W1Ph+UrDQbd0vvpJNJfH3aztN0ON22Hs54P\n2Ynnqt1R+U4a/bmgneXdnKwS0HEvdlkMeC0GIj1tsGGvnHhU6y1mwl6WtrNU6k3W9w/JVshlkhGn\nUZ+VVLGGSS9VgvqcZr63etAlcWaDINMwAWSK8sVPWfmwGHWqJPsBnzr2RDleHXKZ2VYcSyv7Kxxw\nqKbUtBLlR/120mU5IRAQNYXXvRU5kKobsXSBxY0Dro36ZWnzdrP2925LQ7zd57aylSowH0kwHnQQ\nbLfGzvW5qGo4TI+FXLKML1GEOxsJPny+X9MXadTvUGWmNVoiW/t5mcljL5SJ96lChQGPjbGgS9ud\nEoi2yUuqUOFc/+GPVGVkSC/2MgUcGp/VWFB+jr/31TtHErdXFc1mE4fDwS/8wi/wla98hdu3b/Mz\nP/Mz3fifWCzGyMhId/vh4WFisZhqP2+88QZXr17lJ37iJ3j48GH3cUEQ+JEf+RGmp6f57Gc/++JP\n6ITw/l+xTggTExPPLIr+oJEh5bRYNBp9ZgPAVxkdAXWt0aRaa1CtN6hXy6w9fcz58+dPPJD3uGRo\noW2SqBckt+Kl7RwXQ3YeJ4o4zHosPf0al9WI06wnU64z7LEQbROmcb+ddLlGsih5/qwne4mBiNNi\nwG830myJMlff3iAGr81Ipd7kXkx6PxNBBys9k1TDHhuJnpH+kNOC324mlimzsJniZtgD+4d7ngw5\nWd45rEg4zQZVu0sp6p0MOnkYy8gea7RExoMOHGYDJr0OvU6kVK7hMgs0Gk1EQUfIZcZp1mPQ6dHr\nBXSCQMBhZnrMjyBAqwW1ZhOH2YDFqJdVZ0wagat9Lqtqumwy5GJVYyJLS+g7FnCSzFdY2jxALwhM\njwXYOMizr+E5NOJzaFZVRnz2bmbXym4Wj93E60NeVYxKB0ataA5RaqnNTASZj+zLngq5rZo5aCG3\njUyxisdulom0BQFN48Tl7RQfe31I8z0N+ezEeoJk70QSXB4N8GArqWlvAFKLbmU3w6VBNw935J+3\n3SLXPu2mi/znv1vmf/qRq5r7Om0c535QKpVkifVGo5EPf/jDz7WPmzdvEo1GcTgcfPWrX+Unf/In\nWVmRqmjf/e53GRoaIpFI8KM/+qNcvHiRj370o8/9Pl82zsjQC8B7hQy9aELSaDR49OgRoihy69at\nbjWos2i/6mRIFEX2UnmWN+Os7SbZOciyfZBlJ5mlWKmTyhbIFCvwe98EwGzQYzbqKFTqOKzfxWmz\n4HfZGPK7GfS7GBvwM97vY7zfz3DQ/dxGacf9PO9uSzf8Mb+1OyHVyciaCtm74aoA1UaT8YCNpViO\ngR7Rr9tmoNxokshXmQrZeRo/XIAypToBu5H1gxLTYY+stbXTbnuN+W24rUbubh0SEY/Chbr3F/lU\nn4NWS2Qxmu4+1mjIb/zKVsd40MG9nv2bFAnxOkHyMLoZ9qITBArVBplijYfbaZmQeXrMx4Nd+SJu\n0utY25dXhvpcFlkYrICI22aiWm/Q77YScFqwGvUYdAJBp0XmY5SvqMfZvXZ1BXHQqz1SX++5vzTb\nURwDHhshl5W9TEnWxuxzWzTJkLKqlSnWyJbSfOSCNok/avoqkS2xeZBnejzEwvohIVJWeTrwOcys\n7qW5MOihWKl3q0pHOVuDZMI4NeDl6W5a9ni/R06GpPdTxG42Ektpt9VGAk6S+RKPdnMM++yykNyS\nxt/ls99Y4r//wQu4j/AyOk0c5z5bLBbf1mNoaGiIra2t7r+3t7cZGpKT0d4Q6Y9//ON86lOf4uDg\ngEAg0N02FArxiU98grm5uTMy9EHFe4EEdMbrn9eM61lRKBS4d+8eo6OjqmyxDhl83sX+tFGpNVh4\nusXckyj3IrssRXbYzxYRgJGgh2hCXlH40MUR3np0OHFSbTS5MjHA/NMtcqUquVKV2EEWq8nI1+Ye\n9bxS5Mr4IEGPg9kLI8xcGOXa5CBW89v7fhynMpQt17uLeMBu4q0N6RxKtSZTITt3trIEu1NKInaT\nnu+3879iGWnxFoBGs9UlOe4e4W6fS0qwj7TjM3oX2H6nmb18lctDLlbjefyKaaicYnQ9mirhsRoZ\nD9q5v5XG2HPt6gVUY+j7ipF2pbnfZMhBud7E7zBTrTfZ2C+wlsh1CRrAtREPe4rcKqXmxqQXiGbk\nuqN+p1EW5QBSe2kl3hGNl9nLlgkHHF0NSshlYdBrx6jXsaeRoq6VW6blL2TQCaxqaHoGvTbm1hIM\nemz4nRYebEt/R6Wg/HAfauLhs5v4+0c7TE8EWYqmupNmg14bOxpkyOewdM/vzvo+N8eC3NnYRyfA\nmkaVCyRBOEgeRNMTIe60CVTAadEkQ26bifX9HH0uG3azUSbu1tJNJbJlPnS+n7dW9jSPb2hXuFqi\nKGsr6gSBDY3KVLZU44//v3v883/84mM6nhfHjeJ4u1yy2dlZVlZWWF9fZ2hoiM9//vP86Z/+qWyb\nvb09+vr6EASBubk5Wq0Wfr+fYrFIq9XC6XRSLBb5xje+oRJXv1dxRobep3iRZOidTBRP0+foeX8p\n7SZzfOvuKt+8u8p3H6xTrdUZCrjZ2j8kPiLgcVhVZGgpsovLapRHCjzdYrzfx/reocng3bUYQbed\n/WxnMZGciL955ynfvPMUAINOx3/7g5eYnhrhx2YvMujXFug/Lxla2s5JLs5mPZW2DkQHxLIVnGY9\nfQ4T8XbsxoBd4O62dI79LhN7Wenx6bC8nVBop9ybDTqmgg7+YTXZPitRFrMx4LUy7LMxv5lCFA+n\n1EASH/eSmxGvlaDTzEo8x+Jmmgv9Tp7sHf6yHw86WO1pqQUcZlkFCiCWLmPQC1zod2E26DDoYHkn\n280xG/BY2VGQEJ3iWrEYdV1C08H5PjcPY/KKxLDfxW7uQL6vpprMhJyHZCGRq5DIVbiriUtIAAAg\nAElEQVQ24mMrWSDkMDISdFGoNEnkykQ0fHe0vHum+t0sK94PHIat7mRK7GRKXBv1ky5VNcXN5/vd\nPNLYRzjgJJkvsxDZ5+KQl510iVy5xoDHrkmGxgIOUnmJFIqiyOLGPjfGAuTLdVb3MqrtLUa97PGF\n9sj9fCRB+QhtzljQxdLGPvFsiRvjQRY3DqtPR1V/avUmFwa9PNlRn2Oyp5X4ZDfD1XCQe5sHjASc\nbB6Rb/Zg84D9XImg670Vbnqce/w7VYYMBgOf+cxn+LEf+zGazSY/+7M/y6VLl/ijP/ojAD75yU/y\nhS98gT/8wz/EYDBgtVr5/Oc/jyAIxONxPvGJTwBS5+Cnf/qn+fEf//Hjn+BLxBkZeka8F6o9z4NO\ndcZoNL7zxs+Io9piSpwWGXrW9ly2WOHLbz7kq3OPuf1kSyWQ9DltMjIEcC+yy6VwHw83D5OyK7UG\nwyGHwi9FwKbQHVTrTcLjvh4yBA839rgyPsD9dSkwtdFqsRo74C+/e49/9R+/wrXJIX589iL/5Ieu\nMNrnk53f82Cx3SK70GfvVohGfVYCDhPz0QzXh13E8zUMOgG/FXba4/UDLit72RqXB6VR53K7lWbQ\nwXqyiEEncC7kkBGcsYC96yxt0AlYDTq+106mV5KfiaC9G5w64LYw5rfyDyuH5MKpGBv3WOXX8YjP\nykFbnKsT4OqIp6tfedDWBA175ALaIY9VlgQvIKoCX8/3ubi/LV9AtSbLtDxyKqIBkBOivZSa4HQK\nWIlCnURB+nxmJwKIopNUsdpt7VmNelY0qjdKQTVIbTzltkvRJFdHfYRcVhbW92XCbodF+77Q7Pne\nPo6lGfTZcVqM1DQE1YBKLC6KIksbB3z0tUFNMjTR5+bhlpxELkQSXBnxE4mrtwcphLWDxfX9LiHq\n99jY02ghghR9Uq7WMeh1Mh8lu9nIhoJ07udKmAw6gi7rkWQoU6rwh19f5Jf/hx/SfP60cJwKfLFY\nlGmGtPDxj3+cj3/847LHPvnJT3b/+9Of/jSf/vSnVa+bmJhgaWnpud7PewWvVh/jDM+MkyYkvdNi\n72SieFpk6O1G3Vstke8+WOef/v5fMvPzv8sv/V9f53sPN7hxblC17VJkh9fDCt2EAKVaTTX6vBrP\nM97vkz32cCPO1YkB2WPzT7eYGPDLHsuXqrLKxIP1HS6PS69bWovxm5//Jv/8D/8L/+Ov/Qlfe2uZ\nRrN1LDLU7zKTyFe7cRl9ThN3t6Wbfiec9Nqwi1Jdvu9Bt4WNgyJu2yG5Gw/YqdZbXB5y8XAnR6zH\nX6jTBjMbdFzsd/Kop7IzEbTLfI1sRj2CANNhD+lSlZRiCixZkGs3lCP4LVGkz2Xh2pATl1mHXhBY\njKa75GzAbVGFtSqrLBNBp2q/JoP6ltjJ+erAaTGoRuX7XBZVnIfPbmJb0V4TEDV9gKqNFvPr+0QS\nOUb8dmYnAlwe9mhOaWlpiM4PaI/UG/U65tcSXBjwdKf+AOJZdZtOL6Bqne2kipSqNUQtMbIoagqe\nW6JIPFfi9WGf6jktItcSRaqNBi6rtiZnLyM/35XdNP0eG0NHBMBK77tA9CDPjTG58/V4yKX6Du2m\ni1wfC8mIYC/0OoH1RIb/540n7KbVU3mnieO2yc5yydQ4qwy9QJymiPgkRdzPmy12mpUhZdm4Wm/w\nxe8+4E/+dp6dZI5MQa7zeLC+h8dukYTQh3uiquFOu76XZvrcEAsrh2OmgiAQ9Eg3ZZNBj16vw6DX\n4bJbuD45RL3ZpFZvUqnV8bvtRBPp7i/VzUSa2QsjzD3u6I4ECmWJcHXu10trO5iNev7n31oh5HXy\nkak+RicvMhA42ueqg3qzxcOdPFN9dvQCRFPSOdaara5gOJGvMhGwsbiVxWY4XCRSxRp6HRRqTVm4\np9tiZDrsYX4zw6DbItPflOtNnGYDA24L2XJNFnLaSb7vfW+v9TtZ2Exj1AuycXePzShrtzktBlmW\n2aVBF81mi3iu3BUwK92EBz1WmWeR1P6St1R8djNryB+LKgjNqM9ONKmc+nKyuJmSPTbitxNXTHKN\nBZ0qHdBEwKEa7TfqBFZ6qihbyQJbyQIz4wGuj/opVGqstqtFytyx7vkZtBZEsduiexxLYzPpmR4P\nsp3Ma+aknRvwdHO8etHvsbOyl+bKiI/7W4fPD3stbKfVMRh2s4GnO2lMBj0TIZcsy+zgCONEt9VM\npdZUTeL5nRa2FZ9/odJg0Oc48odB0GXtZpgtbSQY9Nq7BFKLjAHcj+4z4NEmCKMBF5GEVC38/a8t\n8ms//RHN7U4Dx02sfzvN0AcVZ5WhZ8TzkprTnig7CULSaDSOlS12mpWhznEL5Sqf/cpb/PA/+wP+\n5R9/leXNBFNDAdVritU6F0ZCqsfXdpNMnx/u/ttiMjA15KdaLjJ9boBL4T4GfC4EAeaebOGyW3gS\n22c5Gufe+i7ffbCOyajn4cYeK7F9tvYz3H6yxZXxAQb9Ti6P93Pr4igmo4FLY/3YzFLbYmMvxcyF\n0e5xS9U654el95dI5/l/31rlf/3MF/iX/+4vicbVC1cvlvcKjHgt3IsdLkbXh11E29Ucj9XAfqFG\ntdGk323uptYHHCY8NiNb6TJ6QT5GbzYIzG92dEWHv+T1AmRLdbx2I0/jBUIKf59e48PrI27W9vNd\nh+pzQYdsAQwrIjnGA3YE4Maol7DPSqXe5H4s293GrBdkeiJQi6DP97lUVZakwgMnHLCrkuv7NGIp\ntJZgLW1Po6H+Dng1vG9GvWbKCjInIAmQ724esBrPMdXn4uqIj8EjFmwlYQPJdfqg53xKtSYLkQQX\nBj14NSajXEe0zuxmA9VGi+XtVNdBGsBzRATHZL+bRkukVGuQKlQY9Erv2WMzqVpUHeTKNTb3c6pq\n0qhf+57zdCdzBAGE4Z7X1Bot2ZRetqidYeawGPE6tCtT/p5r+Yvff0L0iHM4DRynMlQqlc4qQxo4\nI0MvCKdNht7t8Z+nLabEaZKhUqXGH/zVG3zsF/8dv/an3yTeU9aef7rNsEZFZWFlmyHF4w6rCbPR\nwA+8Fmai30et3uRpLMWDWBaD0cjDzTi7qVw3OuEgV5JpGwAebSVw2+WL6V46z362xIP1PeYeR/ne\ng3WcNjOVWp1zgwE+9NooRoMBv+vwZjX/ZIuR0KGD9dyjTb515ykf+V9+h3/2mS8Q2ZFrMDq4u5Xt\n/nrey1ZxmPWUag2S7ZbUqNfK5UEn25mKjNicD9pYarfRxgOHo/c3Rlws9ERw9I6jTwYd1JtNokmJ\naPWSEbfVwGay1DZP9IAodkXYoDYK7G0dmg06fDYTPruJxWiKzVQJr02+CId9ZhnRsRh0KnKk9Mjx\n2U0qTyKtaIqsItFdJ0BEsW+rUa/yBzLpBZ5q6H2UqesAHqd6YRpyGUn3ePA83ctyL5oERG6E/fQO\nzoUDDhIa/kL+Ixb3VKGCTgcXBz2yxxMarTM4bKk1RZE7GwlmJyRyXtQggIDMzTpdqtISW/gcFsaC\nLpXGCMBqMrDaHpm/E0kwM3H44+SoH6H9Hhtzq7uEg2rDTOWi9nAryY2xICaD7sjR/SGfkzuRBKMB\nNflq9NzLGi2Rz3ztjuY+TgPHqQy9k4D6g4ozMvSCcNpk6N0Qklgs9q6yxU6DDLVaIt95tMOP/e+f\n4zf+/O+Y6FfrFVoiBNzqm0CzJRJyOxjwOfnQxVEujfVTqTV481EUsSUS2UvL8qIWV2P0eeU3zdhB\nlumpEdlj+VKVCyNy7dFuKi+rOAEsPNliMOBmbfeAucdR3ny4zrmhABdGQvzAa2H6fS58PeSo0Wox\n4HfRbLX4i+8s8rH/7d/w6//311Vi3d1cldWDEj6rkd1clQshuyyc1WUxdMlNRy8xGbBT6/Hz8bTj\nLS72OSjXmoeeRKLYneYa8ljw243EcxJx0AvIYjzG/Hb63RaGvRYWNtIq3ZWyGhNNFtHrBG6OenBZ\nDDzcyZDo2SapSFM3KBYDrUDVLUVraazHKdps0DHktWHSC1wZ9nB91Md02M+Hxv24rUZmxv1Mj0n/\n+6HzISb7nLw+6GY8aCfgMHNhwK3y7JnS0PAMeW3E0krCIbKhYUzYrzFNaDfrWYjsc2fjgAGPjeth\nPwLyCIteaCW5W4w6VnazJAsVVvYyzE4G2/uwqKIzAAY8NrYUVafbkTg3R71spdQEDFC1tXYzJVxW\nA0atMDZgss8tI9Z31xNdJ+nYEREcQz4HjaaIDjn5ko6nJpybiRwXh3yaGiyQxu1boojLpq52xRTf\nq7+aX2VNQxx+GjjTDJ0czsjQC8JpJ9cfh4wdty2mxMsmQ99/FOW/+5XP8W++dp+9diXo/oakBVLi\n7toOF4YPS/1Ws5HZqRHy5Soeu5W5J1ssb8a77rWLazF8ilDJWqPFkF/9i/T++i4+p7wXf/tJlDEF\nMVuK7MhIWaMlEnDJxaB3V2PkihW+/2iTnWSWdL7MP7p2rpu9dOfpFlPt9l6rJfLn31zgH//SZ/m9\nL/4d5apESr79VKoYDfusjPmsLG5luy0eq1HHTrbc/XcsU8FqgEK1zk6Pf06x2mDYYyGWLsniC0Z9\nVjKlOsNeK+VasyvOBslZujczzG01ki/XiLSjN7Z6RuJ9NpNsRH7UZ2XIa2XAZebOpqRz2c9XZdsr\nKzp7eXn1xqwQQYf9dvbzVYJOM1eGPMyO+bGb9EyGHHhsRqqNJqVqne+vJri/lebuZpKFjQNqjRZz\nkQNuRw6YX5f+V6o1WNxMsryTYX2/wEGhgk6QxNyvD7qZGfMzM+bHZ7eonJwHPWqdxmTIpRnsuqsi\nTTAecNBsM7jtVJHFjQMGPVZMOjXJ8DvMMq1OB1MD3m7URrMlJdi/NuThfJ/6egaOFCmX601eG1Df\nH4Z9dk1x9npbu6T0ggK1eWajJZIrVZnsc2vuC+jeX9YTWW6OH36fA04rOyl1yzBVrODRIDoddJy4\n70cPeK2nVRdy20go/KSaLZHf++rCkft6mTjOaP1Zm0wbZ2ToGXGc6sirVBl6N22xd3vs4yKVL/FP\n/+DL/Is//ir31+UGa8VqnamRoMarpPH0c4N+ZqZGEBC4/XSbtd0U9WZLVbWoN0UmBtVaozurMS4q\ntEbFSl01MSYCNoWZYrnW0CBIse4kGUCt0aS/JzMrmkizmchQqja4fm6YyxOD6HoWlnShzORggN/5\nwrf5kV/8DP/hb+a7polGHRj10AJ2s9LCe3XQyXq7pdXvMrFfqDFg09FqHW5j0EGqWKfRbJGvNsn1\nZGkFnWaGvVZK1TqlWl0mCna1naUFYDbs5elevtsWC/us3VBXkFLsOxWa8YCdUZ+Ne1sZttu6pqBT\n3uoJB2yyVsuQx0KqJG/XbKdK6AU4F3IwO+5jLGDDZTGwn6twfzvNUjTJ/MYBa4l8d5psPOhQpcU3\nNK7hbUWFSZrAyhHPllmOZZhfP2BhfZ8HW0nK1QajPjs3w1JVSWsiS0unMuKzE9Nopwk6rRH/Km88\n3WPCZ2GgR980FtT+IWPQiNRYjqVptFpMahCicl07jd6gg3uxLLOT8u9A/xGaphG/g7nVPa6Pqb+T\nCQ0DykS2zIDHqhlcC8jMERdW40yE3N3jHIVkvsxEn7ri5raZ2UoeEsdKvdE97qBP+3y+thjh8Xby\nyGO9LBxntP5MQK2NMzL0gnDabbLnOf67bYsp8aLJkCiKfPnNZf6rf/Hv+cs3lnEeMZK7sBJjUFHB\nuTLej6DT4bRZmH+6TanHzXZtN8XNc8PK3TD/dJvzSvG1IFBrNNHrBPp9Ti6F+5i9MIJep+NjVye5\ncW6IqxODXBzto9po8NGrk1wcDXFlYoCb54cRgY9dO8dsuy034HdTKNfQ9xCcxdVtLo31d/+9sZfi\n3ICHu6sxHqzvkStW+ei181jak1pLazH8Lju7yRy//id/TXV7mVa1JPnV7JcIOkzE81XOB+0Uqs3u\n4j/gtjA94iaSbTHUE6w6HrDjtOjZy1WxGARZ68ts0FGo1kmV6m290OFCnyvXsRr1XBlysZMtsdfj\nFK3W5Ui5ZtNhL5vJIgd5eZVE6eejzJsK2g9Fv0GnmR+cDBB0miVzv0Se2+tJtlMl2X6m+l0qwbLS\nR8di0PFU4fI8HrTL4jekfbnJKZLRz/e7SRWqtERJ2Hxn44D1eJ47mwf0eyzMjAe4POzFqEMzS6zf\nrV6ozAYdT3fVrZnzAz5EIJIsk8hXeC1kxWoQyOa1/HdETQGzxajj3uYB28kCN8YCssdXd7U0Noct\n0rm1ODM9hKhU0yZPnXOaj8RlBMrv1G7PARQqdWYm1dEg4aBTpqdqiiLNZgujXif7/vTCoNextpvG\nIAgqghUOOmUEOxLPcn081H2dFkQR/vyNx5rPvUwcpzJ01ibTxtlo/XPgeUzvTpsMPQsheVYTxRdx\n7ONiL5Xnlz73N/ztndXuY/c39nh9NMRyNCHbttkS6fM62UnmuD45SL5c5f6GZJrY73VgNOipKxbB\nla0EZqNelqotCEJX1NvvczLkd6PXCaRyZc73u3i8m+u25wCmhgI83ZaHVuaLNfLlCuWexWKi38/6\n3kH3RqwT4IcvT1BuE7S9VI5SpYZOELq5XVvJAk6bhXypwk4yhyiKOO1Wrp/zs7QWY3zATzInLYSN\nbAKxkufNchLRNcSg20K2XKdUa+DqEUzbTXreikgC1t5bf8hh4ntr0sTaRNDBcjuva8hj4clerhvI\najEeXjc2k458tUHIZeJeLMtM2Ess3TvRdFjFEQTJ18egg4XNFHaTntWeCpPTrJdVnPQCrCXkLRAR\nkct9NiotHWv7ecb8tq7pIrTbRfuKnDFFG81q1KuIz9SAm6WofFov4LSqTBq1UuJdGlNW431OFtYr\n7GXK7LVH/kN2Ay6LkeujPh7tZLo6p7TGxNPUgKctoJaj0vN5Nlsij+Il+txWHDYzIK+4jAcdqvff\n3fem1FJd3NhndiLEfGSfc/0eHmypjzkRcstcrW+vxZmd7OP+5oGm2zVAsXpYDZxfS3BlNMD96IHk\neK1BCHWCQCSRpVSpc77fI7Me0DJH3DzIMXuuX7NFBpLZ49NYkqe7aW5O9nEncnivMGtMpcWSeUwG\n3ZFWADazgT//h2V++odf4/ygWp/4snBWGTo5nFWGXhBOmwy90/FPsi2mxIsiQ19+c/n/Z+9NYyRJ\nzzu/X0TkfR+VlXXfXdXVx0zfQ0q7Wq1k0DB0LAT4m2F/EGQJEATCgCTLIGwdFmBZ2gV2KXi5Iqwl\nxcsStbZoCSOJWg5HQ/Hss7q7uru67iszq/K+78wIf4jMrIyMqKGmZ3qKtPoBi5jOzMqIzMqM9/8+\nz//gv/93f6EBQmoJPR7EYLXkNjeXJnm4c8T20cnidpwtcW1Bn4RdqDW5Mn9yu8Uk8drcKB6njY8u\nz3CcKXF/M8qd9QhbR2kOM1VdZ2ojmuLGAJk6kS/pjBh3jtPc7JPRy4rahdo5ynB3/ZDDZJ50scqP\nv36OG0tTeBw2yvUWF6ZPukVHmSLzY0N8b20fs8mEKIpMdZRnggBuh418ZJPq7n1q5SKvjXuI5mpk\nOkDGYZE4yFRodjou0by6EN+Y8mnGWY4OryPssRJymnuKNNDK5hfDLmrNFvsdOX4/idhqOvETGnZb\n+ehsgNs76R7faD7kptXXYZobdms6QfPDbkr1FjaTyLVpP6+Ne1mNFnlyXGYrUURR0HgbgUre7t+/\nCCg6ztG5EY+OAD0Y0wEYKLaUHhemvwYJx6CORgfLb5dYPczwcD+NJAhcnQ5ybTrIrgHXx4hr47Ka\nWDfoFo34HDzcz3Bpws+w96QT5ziFwDxIQL+7k+DiZAC7gfM2oOPQgQqIbp0LGxo/2gciOBQUto4z\nhgaI3Zod9lCoNGjJCsVaXeOYXT8lAHYvke91SQer3zh07ziPs+/5jIjm8XyFa3Nh9k+R0c+EVNL3\nv//q2SrLXknrP7h6BYZeUp01GHo3QBKJRD7QsZjRsT/I116tN/kf/+Pf8iuf+isaLWM573Ysw/L4\nyQ5tKuTj0kyY1d04hYqxt8iTvWP8Lr0SZ+0gwRvnp7gyP4YkCjzeOeLeRoTNWLLnB9Stcr2l4w6B\n6lM0CJLuG0j71w4T+PrOoVJvavhExUqdexsHbMfSlKoNpoc8IKDhJj3aihH0OClUatx5foDdbkW0\nq8fJZTMIVgdytciD7/w9332wisMs9MDK62OenhmjzwLxQp2Lo26eRHOasVim3CDgNCMqisZCwGc3\nc9B5rsvjHkyS2AM3JhG2EyfPsRBSVV7XpnyU+tLKuzW44A+u/yG3jeszfiRJ4MF+BkkSNDyfgNOi\n6wIN5l2dC3vIDgCmwYugZBAyOuqzsz8IogzIz3MhN/GBUZrbbjYccRVrJ9+RSqPFyl4KQVADS2/M\nhnB3IkhEAbYNANK5Ea8maqJb3bftSSRDqdrkxlwIUCgZTrAUNmP67s+TwzS1ZoshA7uBTMn4+1St\nt3QcIoCFEZ8ObFYbbcq1BrlTnqsfcB3nKiyMqDYAkiiwe0psx2TQjdxuGwLHcl8afaZc610rHFaT\noYs2QGkAhPVXF0x99cHumSrLXtR08RUY0tcrMPQe6r2AhrMGQ0bHb7VaPH78mEwm877UYt+v3i0W\n473WRjTFz/zW5/izd9S8m7XDJJdnRwwfmyrW8Dmt3FqaIJLK8aQzEluPpLg6r4/dKNebjPbtnCdD\nXm4tTaKg0Gi1ebgd0+zo04UKl2dHdc9zbyPC3Ki2VZ4tVVkeiPRoyQq+AbVZsVJnYVxLKr2/cajp\n/hSrDRbGhpAVhf1UkdtrB9itFl5fGOfy3Bi1ZovZPnC0fpAARcZqd2J3eRAE9WuuKAr1+A7N6DOa\njTqXx9y98FaAIYfImNfGQbrM7NAJD8htlchUmrgsJo4KdfJ9HJnpoAMFuDbl40msQLTP9Xlh2E11\nwG/owqibB/tZKo22rouzryEndzs4CpfGvSyG3eyni9zfy/QcsQf5Q7Mhl6YL5LRIbB5rwZHHoV3c\nJBG2E9rHnDPgAU349WMFr4E6ycjb51zYo5GOA4x47cSKenRSqjU5zle5u5Og3mhzdTrIzbkQ+YHY\nEKA3Ou0vkyhoMsoqjRb3dhJcmxky7Kgsjvgo1vW3TwccrB6kEYGpPlJywGlj5xTwcJgucndLHZn1\nl9VsvMw4bWbMZsmQl1OoakHmw70E1+eGmR32UKoZ85IAdhMFrs5pAZm5wxfqr5XtOGG3hdlhr+H7\nCGCzmFkaNx6BlTocNFlR+A9n2B16Ja3/4OoVGHpJddZgaLAz1B2LBQKBD3ws9v2O/aL1n765yk//\n5p+wEdWaChardUOVybDXwcKInzvrEZ0y6Dhb1JkiAqwf5/nRC9MsTw1zmMxzZ+OQYrXBylaU5Sn9\nLvfB5iHjQ1pStgKYB95PSRQ4yhS4uTTJ1YUxbixOcuv8FE6bhZ+4co6PLE/zxvkpbi1NoSgKH1me\nZmYkoHaeBIFSra5ZJO6uH3C+73ye7seRRInV3SOG/S4kUdSQvE2CTL1aoVYuIggSbm/XYE9BbjWp\n79xjY+9QAx4kQUESoFhva2ThM0MOgg4zB5kKdrPYk8irvyNwY9rP/YMsw26LJp6jX4r/2oSXw0y5\nF87qc5g146rZIacmj2wu5GJ2yMmE38FqJEex1tRI8s3/CNfphbBb132KDUjWF8NeigOLqxEPaDDD\nDDBUfB0ZKKMGuyKgKsYGK+C0stFHWK632jzYS9GSZS5O+FkcOekqWiRR89hunR/3U67rwYIkChSr\nDa5Ma9WORoAOwG1T//6JQpV0scLCsLpxmhl2GxonTg+5Oe689rtbx1zvAySRU7yChtx2NmJZXp/W\nihMcVpNht+XpYYoRA3uCbh2k1M/W491Ez/UaVL7QoO9UW1GwmURdp7e/8uUaq3tJggNjQZMosJ84\nOb+/vr99asDry64XNV10uU5X3f1TrVcE6pdUZw2G+o8fiUQ4ODj4R2eLfZDHfpFqtWV+54tfZ+0g\noSGIdmsvrs0IC7jtTIZ8PNo9wmW34LJZKNW0i9dRpsgb5ye5/fwQUPk0V2ZHSRTKZMs11g4TJ/OF\nzgOqjaaGvAxqdyfodhBNnYwtQl4nTpuF/+LaAseZEulCmXi2yGEyj91iZiOqJVMPeZ1Uqg0qfaTS\n6bCfSCJLW1bwOe1YzWZ+7PV5SpU66UKFveM09Y7kt3s6B4ksDquZeLZEPFtifizIzaUpVnaOadSq\nuHwBSrkMcq1IAxuiw4tcyZPPprHY7GQ2V1gt5VB8k4iCSEuGww6Y6QanmkQBp1liNaK+3rkhJ087\nMRqSICCJAnf2VC7WuM+uUY4li3UsksjlCQ+xbIWj/Ml9s0EnK4cnrz/otLKbLCMKcGXKh0WS+O72\nyfs25rMT6wMaS2EPT6InC5DdLLI5MNoS0CLmyYCDw0wZn91M0GXDbTMRcFpwWoLIQLst02zLNFpt\nlkY9vd92Wk3Um22uTgWQRFElfksCxVoLq0kinq9SbbaZDDh1fKHTeD2Zst5baHbYTXpHOzYSgJ14\noff45TE/CioYMiJUGwXNAmTLdcr1Jg/3UlydCbF+pHbnYqcEjxbqJ5/5cr3NfqrIfNBKvmAMbMJe\nu4Zf82AnwZXpIZKFKtGM8e/kOq/p/k6c63Nh7ndIzfNhL6sHelf1WrONLMu6JHpQR2SHne9kvSXj\ndVh6eWRGRooA+5kq4aDP8D6bWWInnqPVVrg0HSJdOrHumA552T4+6TS1ZYX/8Hcr/O//7Y8bPtfL\nrBfpDNXrdaxWYwXuP+V61Rl6SXXWYEgUxQ9tLGZ07BftDOXKNf67f/3nfO6tB9zf0kvjuxVN5zFL\nItcWxmnKMo92jwAoVRsaOXp/Pd2P47GbWR7zMRpws7JzRDRV4NlBgitz+jHaXjzHjUW91D6aLvAv\nr8xzY3GcoNtKMl9mZSvKymaM/XiWo0yx15naiKa4taQlU6fyZd2obz+e7ZGpcwQDj6cAACAASURB\nVOUqm9Ek336yy0Eyy/ZRCpNJxGYxc2V6iMWOaWQqX+Zy33lvx9I0WjKtZhPR7qHdbICo7ncatRoC\nApLVidXuoCWoO+LC0S61/VWujFrZzqmfV7dV6gWlXhrzcNiXTG/rEKlNosCtWX8PCIEaANutgNNC\nq60w5rNyfz/L2MCYSR5I+MpXm7w26WXcZ+fBflYDfABd98Y6QO4dJEFLIkSyZRbDbq7PBLg65Wcm\n6MRuFslVGmwnCjw6SLOyn+Hubor7uykeHqheU48PM6wf5Xne+RGAJ5EsK/tp7u0mubuTpNGSeXyQ\nZi9ZpNpo4bObmQu5uD47xLWZINNDLiRBPa/B7tSwx6bjJIHqUzVYS2M+DXBai2V5Hsvid1qYH9Z+\nN9SoEH2HIuSxaVReK3tJfA4rN2aHDENfR/1ODgbk7s22QjTfMIwOAcgMkJAVReHJQYpzI8bfX4/d\noun+PN5P9nhBg3/bbtktJu5sHXNtVt+xDQ90jNYimV53qljVd/VAtStQVWP6482GfT0y/8OduCbE\n1YhA/ld3Nntg7MOsFwFDwHvuJr2sajabZ7pO9tcPxjvyQ1I/TJyhWq1GMpn8UMZig/WiYGj7KM2/\n+u3P862n+4C64xrxGwO4cq3Bj12e5cF2lGJFu8t+sBUl7Ne3gYddVhbHVBlzbKB1H8+VDMdoa5Ek\nHoeVIY+TW0uTnJ8cJlOssH6YZHX3mEzpZGSXKVVZntZfqNcOkhqSNKjhrvMDBo0r21FGAievt95s\nM+R19f77+WGCZ7Es+XKVIZ+TW8tTVBstpsInuWVbsTSCZEKuFqlWKnj8PkRJBT5yrYzQblCv1VEQ\ncLjUY8mVLM8erdCuqu/JzJATWYEb0z5iuWrPvBEgUahhlgSWR7WRF5IIO32y7fMjbjLlGntdVVmf\nr48oaB+7FHYhyzKPD3McZiuE3Vb2+9LjvXZzL7W9W3upQfNDAadF4tK4lxszAW7NBMkUa2wcF7i/\nq4Kew0xZ4y+0OOLVdWg8dv3YZDCfDOBwQMLdBVj3d9W4jP1UEZMk4LCYuDk7xNKot0fsnTIwBgw4\nrawbjL2MRnYWSeTeTpKdZJ6rM0GGO3Eci6M+w3He9JB+tBXLlhEFoUOu1ta43xjwLIz4ubeT7GWT\ndctjM7FtMCZqyQrZcr1niNhfc2EtV6fZlslXagRcNsP8NvX4PlptmXvbx5wb1XZ0Gk19B3kzliXs\ndbBznNXdB6pFRCRdNDSCdPcRp1uywmifE/egJ1X3MX/0dw8Nj/My672OyT4oLuf7qadPn/LOO+/w\n5S9/mc997nN8+ctfZnV1lUrF2Mbgw6pXYOgl1VmCoUgkwsbGBh6P56Woxb5fvQgY+uaTPf7Vb3+B\n3YEL14OtqC5nbGEsiNNm5e5WFJdN3wJvtmWNaivsczI37GYnWeTBboKpkL41fpQpcm0gM8wkiSyO\nD3FtYZxUocyd9QjPD5OAwFGmyFUDaf7d9UMWxrQgp1itszCq5UUoAAMGcPVmm5BPu1A+2T3WnFej\nJTMS9JDOl7n7/IDVnRgOi4U3zk8zMeSlXKsjWE92yYV0GpvdpqrLFBmXx4uAArUigiAimtV2eblU\norb/iFYhiUUSuTbl5d5elgn/CYgbclpIFOssht08juQ1wGIh5KLcaCMKcGPaT6XeotrJMbOZRA2Y\nWRh2Uay1CDgtXJn047SYNX5CEwHtLn9u2KUhSy8Mu3sqrhGPhddGHVTqTerNNk8iOe7tpqm3ZA1v\nbNzvYG9ADTaoFBJQ2BtQow17bLoQ1vlhd88rqFuzIZfOndpqkrizneDuTpL1WA6zJHBx3IfDYtIR\nrWdDbh2R9zQV2fK4j3K9iaLAyl6KXKXGzfmQIZCD0zsjyUKFe9sJrnVCTLtVqOhHeHAygru7Hefy\n2AloXxjxG/KIbCaBpwcpcqVqD7B1y+iKlCxUmRxyETfIFgN1dAUqablcb2LvyOglUTDsiBWqDeaG\n9bYJ3epaBzw7TGmS7UH/HqzsxFUlJxA5pQP01ZUdjk7xOXpZ9SKcIXjviQofVH3pS1/ij/7oj/jt\n3/5t3nzzTVZXV3nrrbf4+Z//eX78x3+cT3/602e2br4CQy+pzgIM9Y/Frl27dmYf+PcKhv7yu8/4\nvT9755SLsICjD/DcWppg7zjLcbZEoVzn4ozeoRZU9+nlyRCvT4dIF6tqJ0JQpdhegzY3wOruMQG3\ng6DHwRvnVV+f+5sx3lnd1XVxAB5sRg1CMgX1fwNv/f3NCNcWxpkfC3JxOszVhXECHgc/ceUct85P\ncXNpiuvnJjBJEv/s8hwzYX+P3Ll3nNHI9B/vHHGlD4itRxIoKERSeWxOF4qsYHV0dvedE5Greaw2\nG/VGC8Gsvv5KqYjD7kC0uajXKohWJ/XIMw6311nZV0cY/SqoqaCduSEnT6J5jWcQgMdmxm01sTzi\nYWU/w1afOeLCsEvTRfLazdyYDlBvtHl4kNXFXpQH1E3tgTFT2GPj5myAqYCD40KdSkNm/bjQO1dJ\ngJ2BTtKYb3AxVnSPOTfi1XgmAUwHXbqFfnDhBNVJebDOjXg1I7Jqo026WOMbazHSpRoTHjPXZ4cI\nuqyGpOfzY74er0Z77toPV6Mlc38nQapQ1RGkg04rmwYdpzG/o+dn9GA3wUTAxbDHjs9hYetY/3hR\ngO2+21ejBa5OqZuU9inf9cWxAC1ZUbtv7RaOjqpMELRxGv1llkSuGozBAGJ93KNYpsTFSfW1zg57\nT1WYtWWl97jBKtTUblKp1mR+5GSDZJZEnXxfUcDrtDLmd5E+xQ5gMujmM19/ZHjfy6yzus6/SG1t\nbfFrv/ZrvPPOO3zhC1/gk5/8JJ/5zGe4e/cub731FvV6nS9+8Ytncm6vCNTvoX6Qx2TFYpHV1VWm\npqaYmJig1WqdWVDsewFDn3vrAb/5hbdQFDUqYzBjDFQ/oNfnRhFFgTvrUc19K1sxhn1OEgO7yaXJ\nEEq7yaOI/qK7uhfn8swIq3vaYwXcDhbHh/jG6k6PaK2WgGSw+2q2ZTx2iy5SIV+q8xNXFijXGjSa\nbTLFKrF0nkS+Qjxb1Lhe2y0mPA4r8T4ia8BlpyXLVOpN3E4bPpeTyWEPtUaL42SaZLHOYSqH02bp\n+ac87/gV5Urq80gOB5LDS7tapFIuY3f7qBZzQBVsbiRk2s0G5WoVpVlDtHuQmzUEQWB38zmiO4Vt\ndKk3jrKaRETgWYc8PR9y9/4b1N26mjCfZ2nEzXqfpL0/OPXcsItitcXzjuOzRRLY7FOFua0mDRG6\ne7/DIrE84iVXbbCfKhHpU4VZBswEF0e9rEW1i1lygNOyNOplLab9bBh1VvSeOvruESiGRotGAGci\n6OIoV0FR4DDf4DCfZMhtUwn9U0GeRDI9UGc3MBC0myWex/Rjn/Njfp5FVP7WpckAqWKd43yF2WEP\n6Z2E7vHjAafGrXknnsfnsPL6TJBvPIvpHn9u1M/zqNaRe2U/zRsLwzw5NB5D9UdjJEoNlsZ8bMfz\njHhsvey5wao3Wqweprg0NcSTPoL4qN+pI2Lf2z7m0uSQ4fvUrUypSrXexCyJGmDqtJo47PsMPdiO\nMzXk5iBVZDbsZWPgtQI83kvyLy5MaEBZf7lsFv7Td57zy//VdfynbLjOuprN5odKmRis3/qt39L8\nu9VqUa1WsdvteDwePv7xj5/Rmb3qDL20+jDBUCQSYXV1tWei+GEff7D+MWBIURT+7Ve+zf/y+bd6\nO+9BBVi3RgMeLCaJla0j3X2NlsxkSLuru74wxnokxfOjgqG/EKgk5e7FejTg5sbiBNFUgbcfbRt2\ngTZiaW4akKm34wWuL4xy/dwEN5cmGQ96SRXK3F47ZDuWYWU7xn4iS7MtE03luX5OO1qrNlq60Vim\nVGVxYggEgWKlzs5xmm882qFYqbOfKlOtt3DbbbxxfprX5sawmCWKlToB7wlZtVKpoCgKgigi2T00\nG3UkqXMRrBVxupyIdje0Gnj9QeRqAUky4Quor10uprDk9siXVY7QfMjBZl+3pz9p/MKYm+dH+Z7H\nkNumvdgeZipYTQI3ZlTZ9/O+6IvFEY/Gi2hu2KXpRl2e8LE86kGRFe7vp2m02hogJApwmNUClkHn\n5DG/XTciG+TiGHWKRn12nQfR4oiX1ACwOhf26owWgy6rofT92EB6PxNy8Sya5eFBCpfdzM25EJMB\nB1sGo5+lMd+pLs/denKYIVeucXMupMne6y+jCIxcpU6mWOf67LtzaPqrVGtxYcKvu10S0Mnj12M5\nLk+FGAvqOUSgAt/1aAYUOEgWGPaedPPGA8ZS8Fi2rIm40Zxzh6QdyZR6WWPdmhro+MmKgrsTo+Jz\nnK60erf9cLFWp1Jv8fl3Vk9/0BnXWUdxPH36lE996lP87d/+LalUii9+8Yv8wR/8AX/+539+ZufU\nrVdg6CXVhwFG3k0tdpat0+8HhmRZ4be+8HX+7Ve+rbl99zjLtQUteFmaGKLaaHJ3M8rVeb3hIagj\nsbmRANMhDwGnlftbR3RZCcdZY2L0YarAR5enubk0SSJX5t5GtKNvEmi3FcOL3kY0jbtzofQ6bdxc\nmmQu7GEvkWftIMHd9QjRdAEQKNebTIT0F/17GxFmwtrF48lenOsDfKV7GxGtwaMgkC1VsZhEFGDv\nOMvbD7dotmREQeTK/DilWhPBekJ+lWslTJJEu1qg1Wzh9vmhY8BYq1SR6yUEm4tarYYgmWjXK+Ry\nOQSruvDUihlq+4+Y85mpNdvk+sJO4x2Z/NUpH3aTSLmPPxQvnIx2JgN2vA4zQy4r9/YyjA2ofnRS\ncEX9v0vjXs6PuFEUhQf7mR5gCg+MJeeGHBrTQNFgRDY+cEz1MVpwtDTq05GpJwyIxEagwMirx4gD\nNBNyG3aQ+uMgcuU6d3cSeB0WpgJOlka1nyF50ECLrtGiFnjUmm12jvM0Wm1dkvuoz8GOARfJbTfz\nLJrh3k6i4yR9cqxBdVm3bBapY7SoBRvnRv0UDLhKK7uJU00Y58LeniKxUGngMAm9DYsRQRqg2mie\nqj7rN1R8vJfQKM6MfufpQYpLk0FNjtpgrccyLI7pwZ9JFNjt/A2+9I2np4LQs66zBEPZbJbf+I3f\n4M033+T3f//3+ZVf+RW+8pWvYLfb+cxnPsMnPvGJMzmvbr0CQy+p3kuo64tUsVjsmSi+9tprZ9r6\nHKx3A0NtWeZ/+/I7/Mlbxq6tx9lS7wJ4bWGMnWN1lwuQyJdPSaUWmBr2cZgqEi9od+1HmaIug0wS\nBd5YmmQ9mmIzktI5GW8fZ3TZYqCGTd5amuTy7AjFap27GxF2EkXSxRqXDFyxH27HeH1Ast+WFcwm\nSQe2NmPpAcWZQDxbwmE9WWiPMkXm+uXUgkC+UkNR1GMlMzloN3G4PR1QpGCzd9r1SptcJoVgdeL0\n+Gg06gg2N0q9RKNRx+tX+R+K3AZJRLR7qFWrOG1mVr73D9iUkwUi7LYSyVW5Me1nZT+rSawPu609\nc0RJVH2JthPFXteoVO9f1BT2+8CBJChYTAJTASdPojk24wWdiiwx8Pe1D4CpxbBHp6jq7+QEnBau\nzQSYCDi4PhPk5pz6M+q1c206yNWpAFenAlyZCmASBfUxs0OdnyAmSWBxxEvIbUUUusBKDyyyJT3X\nZ8hgdDIVdBnmm5lEkdXDDOuxHOfCHl6bDOKyGo/Ilsf9FKr6xXc27GHrOE8iV+kowNS/04SB4SOo\nbtRd/547W3Fen1aJ1bPDHuJ5fUdLFGCnwyMadJ4e7A52a8ht51trMV6f1nefXDZtR2YvVeZ82IUk\nqhsRo1oY8XFvO87lqSHdff3j01qzzbDnBAQY5ZGBam+wb/D3BAh5HBxlSoZxHzPhk45drlzny99a\nM3yOD7JeZH05yyiOZDJJMpnkb/7mb/jsZz/Ld77zHf7yL/+ST3ziE3z2s5/l7bffBjgzescPzgr6\nQ1DvpdvyMjszH7aJ4nut08CQLCv8xn/8O/78m6tcngn3EuT7K5YpcvPcOKIoqLydvrcxmi5w69wE\ndzYivdtcNgszYR/vPN7l3IhXE0XQraf7cXwuG7lSjaWJIWqNNrfXVU7QzcUJ7q5HdL+zHkniddrI\nl2t4HFaWp4bZPsrw9YfbnBsL6hyu73RUZFuanCeBaDqPw2rW7BQPk3n++aU5sqUKFpOp5zTttJp7\no8Lux8dpNVOs1Kk2mhQqdfZSeRYnQmxEVEPCWLrAhfETvgjtFmbJRKVRBLOFpgyCzYVSKwECVlGh\nXCwgWJ0orRZmi41mo0YuncTu8VMt5lGqRZBMePwBCsUiNJusfO9bmMYvINrdTATsjPvt3NvLqHEW\nA0qweLHOqNeG3SwRy1Z775XbZtK4Rs+H3GwniwgovD7pxyKJ3N49MdtbGvHwrI/XM+5zcNCn2BJQ\nOBjgnrg6i3DIbWXUa8dtN1OoNpgOOlU35VKd6SEnjw9POCEmUcBhkTSAYnrIxcMBkHJxws/TiPb3\nrswEqdZbzA+7acoymVIDRZF1KjAB2DMI/Qx77RwM2Dy4rCbWoiegp/uZ/pFzYcqNFo/2U/R/MQaD\nVrvVJV/XW23ubse5MBEgWayemi1WGTA4fbiX5Nyoj6DLZqjWWgh7NZlrd7eOubkQ5u52gsgpqqqZ\nYQ+pQoX1WIbZkIfdvvfEyKfn6VGBH1ue4B+eHeruA9WJHOAoV8JpM2u8mqID5/B4P8lr0yH2UwWd\nNcLJ84ksjQW4v6O/Nk0EXSTzJZ4dplkaD7IeO/ksDJLqP/P1x/w3/+KioYfRB1Uv6j5tt+vzGD+M\nqtVqvU374eEhi4uLvfuSyeSZr2WvwNAPUbVaLZ49ewbArVu3fqC6Qf1lBIZkWeF/+qwKhIBT28iC\nAGaTxP2tiKH+dusojd1qplpvMhP2Ua03ebKvEkSrTRlRQAdUSrUmH12epNlqc29TS8C+uxFhfjSg\nSbQHKJTr/LOL09SbbR7tHHH7eRcwCbRlRedMDapSbfD2erPNRy/MUK7WqTVbJHNlouk8dzci+Jx2\njjL9C4DClfkxHm73EVgVhYvTYZ7ux3uPqTXavDY3hlkSyBeKJEt1xkJ+Ykl1Ac3nswgWB0qjQq3V\nBEHC7fNTKZepVSu4PB5KhTwoCq5AkGy2gYAM7SaYLAiAx2kjn8sgWp1IVjvNUp7WwSqu6UuI+Li7\nrx7r3LBbwwGqN9tcmfSyeVykZhI1Hj3zIRcPD04Wz4DTgsPiJVdpsHKQ5fq0dvzQz0sCGPXbifa7\nUI94eX6kvo7ZkIshl5VGq03AaSZZrJEs1rgxG+RxH8HXLAk6Ls/yuI/VA+3fP+S2sT8AhroLb7da\nskK7JfM0ou3WvDEfwm424XVYKNWb7MYLzIQ8rOm6OmrW3GAtjfq4v5vU3Z4p13kezTIf9mI1SzyL\nZrGZRcNu0ZjfqVOFPYtkmA25cRpEUHgdFjYMnmfzKIdjSvUyShSMgWd/3d2K88/Pj/HN51HdfaCG\nLgPUGi0q9SZ+p5Vsua6Sl40S4hVotloE3XbSRT3PaS+unnOyUOX1qSCPO3/HEZ/TkOicyFeYH/Hx\nYFsPdgB8Tiu78Rw2s6TjZol9HSFxYLM7mPsWz5X5qzub/Nc/ct7wOB9EvQgYOstcsmazSSqV4tOf\n/jRPnjwhk8nw+c9/HkEQWFtbO3MjyFdjsh+S+kEeiw3WYFdMURT+589/jT/7xuPebdtHGR0HyCSJ\nXJkb5TtrB4aO0KCSi1+bHeHawhixVEHjSRJJFzXJ9d26NBNmM5oimTf2LxkMihzyOLi5OMF31/bJ\nlqo6k7Wd4yw3l/Rk6p3jDLfOT3JhOswb56dYGAtSrNb5+soW2XKNh9tHPU5RrdHC79bL8vfjOXzO\nvnGKIJAsVHD27AUEDpI5RBTub8bYihdJ5quUak1cXj+SzYUgSEhK++TiorQBgXariWB3U683wGRR\neUjZDILNjWB1UqtWEE0WaDdoKyBYHMj1MoKsgiTkNmQOWFnf752eqy/DzGZSlWMPD3KUG21mQ04N\nMO3HjgvDLsr1Jo8jOQ4ylY6nzsniZcTrSRVPRk8+h5lRr50LI07cVondZIlyvcWjw6wmADaa0Y53\nlsd8A6M6PeY2Gn25bSaeRbVgwWU1sRbTcnUEVM7S+lGOO9sJnkWyNGWFkMfKzbkQ431O3JNeiw5g\nAJQMNgphr531DljZjud5FsmwPObj5tywJky4W6cZJw65bTzaT3Jjblgz7pkPe3VhsgCzIU+nE6Uw\n3j9eUxQOUsbdlXqrbTgGc1rNmm5KPF9h2GPHJAqEvafzWCLpEmGvXTdaHg+4SJdP3qtHB2mmA+p3\nJ+g0vj4e58q4DbzJulWsNkgWqrxmcP5HfeBqLZJiaUy91pxmFfB/fu2RIcfrg6oXcZ8ul8tnxhma\nmJjgF3/xF8lkMoTDYX7u536Ohw8fcu/ePY6Pj/mpn/op4Oz4rj+4K+r/T0pRlPf9x30/Y7EP4vjv\npxRF4Te/8BZffFvvzpoqVHpZW1azxOJ4iJVtVTH27CCB226lWNVzLxRFYTOS0MQ/dOsgXeyNpSwm\niSvzo9zpjMGGfcaKlPVoiuvnxtmIJLkwHWZlO8bdTfV3FBRNHli3VnfjhLzOHsBangzhslvZjKUx\nSxLPDrpyZtV3qFRrYDFJGmC1dpDg1vlJ7vTJ+LOlKtcWxniwdbKzTuRK3Fic4N76yeMe7hyzPDXM\nWuc4hVIF0e5Grnek8FYbZquHXDYDcptiPotodSLXSjQVBcnhQRCg1WygNGvQViM8pHadBgKlfA7B\n7gZBoFGrYnZ6EZoSpXwGoVrFEl5Acvp6WWQjHivzIRff3joZc/Wb3ZlENVjV77AwM+QgWaix2acK\nWxzxqF2e7r/Dbp73SfdHvXby5QbXpwNUGi224gUeHqTJ9gGfQWLu/LBbZ5jIQAyIx2bSyfCXx3y6\nbs/iiJf7e9q8LKMOzvkxnw40mSWBuzvJHmiZDLgY8TmolYscDqyhYa9dM3rq1nTQRXxAibYWzXJ5\nMsD12SG24wUNV+o0F+duuOzd7TjnRn0UKnUShZohoAIY8tjYTeRJ5Kv4nVbmhj3sJApM+G1Essbj\ntmS+TDRT4vyYX9O1Ojfq4+GuVua/HstyfT58qjHkiM/RC2C9dW6Uu1sndhijfqcuBLauiO8qtQc4\nSOYZcls14BrUa9BWJ93+eSSNx27pkcCH3HaNFQFAd68xGfRwkNSDod14jq892uW/vDr3rufzovUi\nYOgsOUPhcJhf/dVf/b6POzN/vDM56g9pvdc/0vslUb/fbLEPKj3+/dS/+X++yVfvbRred5jMc31h\nHIfVzOxIQOP7U6w2uDCQGm8xSVyeHubORtRQ/q7+XpPLMyPMjvgJ+109IATw7CDJlTm9Ik0QwGox\n4bBZuL1+qAEs20cZQ0l9pd5kYSzI69Mhhtx21g6T3N2IkC5UCHr0O69oqsDVBX2368nusS5y5MFW\nVOdufW/9kEv9BpOCQKZU7esYgVwt4OxEbFTKRfLpFILZhsvtRbA6kVsNREkCQaBdLWJ3uhDtHmi3\ncHl8yNUiTVnB7vaCIKDUSoh2H6LJTLNSoCEr2J1uBNFEPfIEHxUi2SoXRt1U6m2NI7XNJGr8gxbD\nbs6Pemi02qzsZxkZMEF0Dixg3VGOSRS4MunnXNhNvlrn/l6atViexbBHC4RMIhvHWuDjG1B5eWwm\nnbfQoDEiYKg+HMxGAwzVUkYqpQvjfg3YOMyUeHKYZjNVZSrg5OZsqJd3ZWTyCOjcrQGCbivPIhnu\n7ySRZYXrcyFEAWaHPYacnfmwR8Oj2TzKUWu2uT4b6nWdBuuwb4yXLdeJ5yucH/Pjthovwl0zx0ZL\nJpIuMh36/teszVj2VML1RPDk91d24kyHTgQERgDuKFvm4lRQwy3rL7/DxG4iT8ChP9582Nf7LBSq\nDZb6usyTQ/rXsXaY5vx4gOF36Wr9zf3tU+97v/UiY7KzltbLstz7URSl9/ODUK/A0Eus9yOv/yDG\nYmedj/bZ/3yf/+OvbjNlkE3UrUypymTI24m50NbKdoyQV93FeB1WxgMuVvfVxz3aSzBlIF3vVqPZ\n4tBgtxbPljD3kRpnwn4WRof4zrMDneS9W2uHCfx9Sq+FsSBXF8b47toB9Vab1ACX4el+nBvn9FEd\nd9YjmqgOn9PG/FiQC9PDvHF+kmsL4yxPDTMV8nGcLjAx5MVls+CxW3E5rBylc0wNObkwPcyNxQlm\nRgK8sTzFZDjQkcwL1OsNBLHz+gQBQW5Rq5ShUUUQJby+gAqIgHKpiNyogcmMiIJosUOrSbWQQ3J0\nvJuaFUTRhGCyIpgsVKtlZFlGMFs53lhh3tVi/bhIsdZkt29ssjhykl02F3Litpq4v5eh3BlR9Su8\nBBR2NdwZhUq9xY2ZAC6rxMODDPupkmbkNijJPz/q7T03GEvsjYBPcUCF5bBIPB8YfY35HWwM8G/G\n/Q4dWX+Q+NwtI9C0PO6j1lI4SJe4u5MgX65xacKPJAz6S6smkjGDTs9cyNtTQhaqDe5vJ5gecjN5\nilrMZ+Ccna80EAS4ZuAttBD26nyRyrUme4n8qQtYvx9QqdakVG0Q9jowiQLbR8aAa2HEx6O9JPNh\n/fe5n1vYbMuqu7pJwmo66eIMVqZUI+w1fg/mOpuojXiJSb9W3TfIpXq0GyfU2dgYilhRx6KDatT+\nOsoUubupN7H8IOpFOkNnyRkCdYPe/REEoffzg1CvwNBLrBcFI0Ymii9SZ9kZ+u5Wkt/5kiqVfLAZ\nY9wgfd5psyAJAl6HsVtroyUzPawmzFsksRcfAOqww+fW7nDMJpHlMR+3NyKETwl4PcqWuL4whtVs\n4o3zkxwkcmx2FGB3NyJMDetzy4rVBnOjfl6bHWF5KsRWLM3KdgwEgUShYtiWX4+mNAAKYH4syFjQ\nw5X5MYa8DnLlGk/24vz9ox1AYGU7yvPDBIepPMe5EgG3g1KtQaFap1Rt4glU9wAAIABJREFUkC41\nsJhMPDtIcG8zwu3nB7z9cItaG1BkRLMFu92OYHNjs6vvjdJqYnd1FqhWg2w6BRY7ok0N7xRMFmg1\nKRQKyIKoEqgFAaXVxGxXk9dlyaL+W1AQTFZoVBDNNmS5zer92zRKORbCbrKVk4VLEgXMksCNaT8H\nqbKmSzTqtbHbF7R6bsTT4/lcGPXwI/Mh1mJqxliu0mQq6NQEtxp1gQY9fZbH9CGsg92dEY+Vo1wZ\nv8Oiqs98dl6fDOC1Wwg4rDitJiQBDc+nW4N+SaCOzQZJt5NBp6HCsVDRnktbVmi2Zb67eUzYa+fG\nXKhnDHkax8VoFHaYKvLkIMWNuZDG+dvIBLFbmVKNu9txrs2GNCRxv8vYfHAi6GI7WebihJ6fN0hy\nThdV087L0yHD7hqodhuNlkyp1sDT181zWE1sxLTE9v1UgcvTQywYvNfdCrpsNNttQwl8f7SLIJk0\nROhYSguuGi2ZqU5HKH7K2HEtkqZlENzarcNk4aVFdLyomszlMqYL/FOvV2DoPdR7RbDvFQy937HY\n+z3+B1XferLHv397s9fulxUYGXCQtVtMTA552Ypl2D5KYztlzp8pVDAj6+IUQM3oWp5Sd7Qhr5Op\nkI+1Du/kwVaMpQm99wioO9bZET+3n0c03QZZwTD4dWkiRL5cpyXLrB0mNYzbTKnO4ph+UShW6iyM\nB7l+bpzrC+P4nDa2Ymn+4ckeVrOJ1IBvy8PtmM6kcXXvmEsDuUpb8YLWxVoQSOUKYDIjtxoUi3nk\nSg7JbMZssSLaXFTrrZ4ZoyAIyI06QquGoihIJhMubwcANqpIFjsmuxulWcVkMqEgIMttBMlMo1pC\nMNtBgHY5p47YFJlGYpda9oQLIgrQasuE3Tbu7WWYD7k0pOYxvxYkem0mrkz6mQ06eRbL65Q5YY8W\nLJ8f9Wi6QE6LqOEbAVgkiSGXlfOjXq7PBvmRhSHsZpHFsIdxnx231cRk0EWx2iRbrpMs1DjKVkiX\nasQLFTKVmhqGikIsU2bEY2Mx7OH1yQA3Z4cwSyIXJ/wdE0j1Q5QzyNYbMRihTAVdhu7Sjs6I7Tin\nBqiiKLwxP6zrPILa5TIahV2YCJDugJuAy8pSJ939/LifrEHO2WTQxXbnXB7sJpgZVo1LBWBXx7dS\ny++00pQVNo8zXJw8+eyHvQ5DCX4kXcJtM+kNNlHDV9c70RfxXIXJoKv39VoY8ek6eaBK+I3y4bqV\nLVXZS+S5OqfNLRQFgZ3ECSA8SBW5OqeO4l02M0d5/fvzYOeYc2EPkVMiOEb8TmTFeMM5HnCRLlX5\n+8f7uqyzD6JetDN0lmMyo9ra2uKdd94hmzXu9H1Y9QoMvcR6L2DkZajFzqIztLoX5xf/8P/VtY4f\nbMZ6afEWk8TcSID1iEpIzRRrvD6r5/LMDns5yhTxuE/ZyQgCjZbM0kSItqKw3Z94Lwi6cxAEeOP8\nJE/3EzitxhfTZwfJnknjeKeLsx5JsnWUIV+pa0Zs3Xq0n2BxfKh3jEvTYa6dG+fhdoy2LHN/K9oz\njgTVk+jcuBaoNVptbGazzlRy8zjHxJAWJD3di2s6bYrcRjT1tfgFgUqpRFtWkGsl2vUKSr1KIBBA\nsNgR5LZ6QVRkWpUC5WJRBTaoXCKl3cTqcNFoNGi3FWhUwGIHBORqHrsnoIbetpoINjdyrcje7hZy\nvYIkKFwMSjyJ5HqxGYPp8NkO0VcU4NqUn3ihxsODDLupktrBGFByHQ4owgY/0rNBOwGnhdcnA1yf\nCXJhzMt2Ik+qVOP5UY77uymabZlHBxk2jvNEsxVKtQZ7A2O0yaBTNw67MO4nmi1znK+ycZzn0UGa\naqPFtzeOeXKY4ThfwWqSuDYTxOuwcH12qGNqqHRI43pwMJjgDqr7c7+HEUC53qLRahNLl7gxFyLU\nBwo9duNuUX+HLJYts36U4fpcCIsBDwpUCXp/bR7lMEkCH1kcMQRhqlpOXdgbLZnNo0yvQzQ1ZPw9\nFVDdnS9O6Hl+i2N+TYfn6UGaGx3zxkGVZ3+lCtVefEZ/eR1WtjodsCf7CY1KbTbspTBgyLlznMNl\nMzMX9um6i6AKJ07jMwGMB9w8PUhpgl67NdJR9MmKwp+8hO6QLMsvpCY7yzFZf3XXxufPn/M7v/M7\nfOxjH+OrX/3qmZ3PKzD0HutlhLV+UGOxwfqwwVAkled//dLbGuOzkxIIehyqqdlEiGcHWo7QWkc9\n1q2ZkJtYpkS1KfNkP8HShJ7TAGoshtNuJmNw4d46yvS4OyGvk/MTIW6vR1CA+1tqqr1RJfNlPnp+\nkuNsiYfbJ9Ee0VRBFxfSfW1Ws4mPLE8R8rl5cpDgwVaMZlthP57XSuVR+wjVRgurWXuR3YqlubE4\nictmIeyxcX5iiNfmxpgfC/LRC9N8ZHmKixMBLs+OMjca5CPL08xPhBGsTmxmCbvn5IKsKDKyKJ24\nNwoK1XoDpVEFkxkECa/P33usIrfAbMbt8SBJEvVKCVoNBJtTTUmvFvD4gyAIVKsV3L4AtNSdtN3t\no9Fo0og8YcwlYXG6TzRbCmz1qaNCbgs7iSKvT/oY9dop11sc9I3Azo96yfWNkBaG3Rz35X65rSae\nH+UJOK1cnfZzcdRFrdnmOF/l4UGae7sprGaJfB8XSEBhL6ntolyc8Ou6jYNRH6fV4JpZa7YRgPu7\nSe7vJolkSnjsZn5kMcx82KORuZslfXQGqCO2fvVdt4rVBs22zL3tBLlSnRtzIcb8Dp4bcJMCLivP\nIlqnZkWB9WiGXKXOzPBgp1lh34BXlyhUkWXZcAx2fsKvcW9utGS2jrNcnAiQPcXMcWlM/Z2V3QS3\n5rXdGiPDyPvbcS5NBtk7pZsyGXSzFklzzgCAzIW9PT5TtdnWRHAE3fpxfLZcY3kiiPVdzBEFyWQI\ndkAlJINeAACg9G3GvvK9DTIl43DaF612u/1CPkNn2RnqJ0x3gdxP//RP8/bbb/Od73yHn/zJnzyz\nc3sFhl5ifT8w9EGPxd7r8T/IKtca/MK/+wqFivEFEdSx1q3FCZ4YOE/3q8dmhpwcZSs9Ai4Yq/Le\nWJrgwVaMSLJ4aj7RbkLNO6u32qxF+qTRgkC12dKZp702O0K12ULGmBh5fyPKZN84a9jr4LXpEGuH\nSRRUGXx/ZcvVHmmzvyKpPFfmRwl5nVyZH+Mjy1Ncnh1h7SCO124mXqjzPJLm3kaUf1jdQ1Hg9vND\nnkWz3NuM8q2n+ygKbEcSKPUKlXKZaiEPFgcOpxPB6kKUTLi8/h4gqlbKCDY3tJqUCjnyuRwmhxfR\nbEFpVJHMVorFAk1FQLB7VcVHNY/g9CJKEsViEcHsAFmm1pDVOI92k1q5iMtuRTCZWX94m50+YutC\n2EW+frLIh+0KIy4Tjw6yRLMVjU8R6InRPufJ7n92yMmN2QBjPjuZco2V/QypUp3NpLZzNCjTvjCu\nBz7iAE1ZBSlaYDDssekI0SNeu04677BIOkPFQrVJMl/l3naCaKbEiNfOjdkQHz0XNtwsDMrmQc03\n6zdO7IKiUa+DCxN+HAML8HzYY/iZXRrzs5PIE8uUuNGXIXZ+PGDoc2Q1iTw5TLN+lNURqwePCaqv\nUK5SMxyDgbYzeGfrmKud55REga1jPaiTFYW2LGtMDvtrtAMuH+zEeW16cBSuff1d12lQyeJGtbJz\nTKmmH5F1K5LMYzMbd4cSnRy+x/tJRjzabnO/6WOt2eL/+sbTU4/xIvUinaGzlNYDPcJ0tVplb2+P\nBw8e8Md//McsLy/z5ptvYjabz0xd9goMvcR6NzDyYZgoiqL4oYAhWVb4Hz7916wdJnkeSXFpetjw\ncdfPjVM8JZkeVN7M+RE30WytDwiptRFNa2Txt5YmuL0eBQQS+fKp6fTnxoYwmyQKBnyOvXiOGx3Z\nvM9p49rCGI93j0nlK9xZjzI3oleXtWQFp83C9LCP6wvjJPNVHu+naMkK9zaihoq0B1tRrnQMJiVR\n4MKUqh47SOYJ+V083Dnie88PWd2LU6g2kQUT9gFly+3nB1yaDutuszr6RhOCgKi0qdcaKPUycq1M\nKZ/F6nBhc7nVWI5mDbvzhD9kUlrIrSaS3YVJaSGYrCiNCkq1gNnpBURMzRpWmw1BkBAkCYtJotlS\n/YkkkwWfL0Axn0URzCjNGrH1FZS2yunpyttHvDYujnupKhaOiup9IorGh8YqCaz3cX9EQXUqvjET\nVEnXyRKRbEWTZxYeWIAm/A42B7gug6PHgMOiAzQXJwIat2yA6SG3DlxMBFy6ccqFcb+GwwQqL6gf\nIB3nKtzbSRDPVnBYTFybDjLtU7k5iyNewwDXgEGWGUCuWufOdhyrReTaXKgH6wbjJ7qV7nQkGi25\nk+MVxOOwGAIbgOWJIOVak1ZbZmUv0cscM4mCoUs1qI7Xe8m8ThEmgI5H9PQgxeKoTw1zPQWguGxm\ngi6bkQm9ZuQcTZd6pGtREAy5OUfZIkG3Xecy3y2v03bqZmos4CKer/D0INkzWey/L93XDQsHTkbX\nPruJ45yWdP2lbzyhfkrg7IvUi3SGzlJaX6lUWFtb48033+QP//AP+fVf/3Vu3LjB1772Nb70pS+d\nueniKzD0Huv9jskURXlpYzGj438YY7J//X9/k//8YKv377qBuuKN85Pc3Yyyuhs/ldg85rPjdnsM\nSZMAybyq3Lo2P8adda3d/6OdYwJ9js52i4krc6N87/khK9sxRk9Rl60dJnhjaQIEgQfbR70uigKI\nkqhzvQ247bjsNoY8Tu5vxTT70LasIEmirtskiAJmk4mPLE/jsFl4dpjk9nqEo2yJZK6Ca4D7cJQt\ncmEA+IBALFPEbT8BSYIg0GrUQTpZ1ORWE8Vk1fxevVqj3VABEnILFEU1VJRM1GtVJJsbuVamXquh\nSGbVbVoUaDYb2J1OWgg0FRGl3eiRrmk1sDs9tGtldXESTcjVHB6fH7lepn68haLIxPM1bswGSJfr\npEs1TfDq8riPcvPkHZz0mqk02jjMAq+Pu3ljLsiTSI57uymOctWOnL3Q98oUDgeyyUYHyNl+A+Az\nH/bo3JZrA4uUKKBRLwKncoCSBiPaYY8eyMyG3Kwf5ShUGzzYS7GfrRF0WZkIOBkbUKzZLRJrEf3i\nPdcJXwWVvH9/J8FUyM2PLo4QNfDWmQt7dK9j9SCFx24+dWFu9nF4FAXubh9zcz7M8kTg1M1MPFeh\nUm+RKlZ7CixQu1KDWWiNlkyyUMXvPN0JOpou8jya4eaCNgDZ57Sy2Td2TRerzHesO+bC3l4eW38l\nC1UuTAYMHbYBpkMeHu4mdGAHYMx/stkYbFSN+rUcqdW9JGMdocjsiLHS7gtfu0+z+cEk2r8ogfqs\n1GS/93u/x8/+7M/yu7/7u9Trdf70T/+Uj33sY/zyL/8y169fx2zWx8R8mPUKDL3EGgRDrVaL1dXV\nlzYW+37Hfxn1F99+yqf++rbmts1YmvnwyWu7vjCmhq4CCMaeHdNDLuLFOg+2Y0wM6WX4AOlihTeW\nplTQMlDVRqtnxBj2uwj73TzcUR/XaMmEDeIJbBaTSr6WFc1us1tbsQw3zqlg1WySeOP8JLVmi3ub\nUTZiaUNzxe1YphfVMeRx8MbSJCGvi7sbUWrNlm6EkyyUde11gPsbkR6RG1QyqdVsYiHs4/KMStCe\nGQthtTsQLE4sDjdOlyqpV+QWgq3vgqf0EawFgWqtBooM7RYWhwuHWUSwONQWdqOCIFnx+PxISou6\nLKC0GrQUECx2qJdpiyYEFKqFDB6vH5pVRJsLBIlKtY5gddIupgnUjqk0mtzdTdNoyTqJ+uBYZSTg\n4eqUn7YCj6IFEhntIj46YNS4PO4n0xfHIAmwHdeSohfCblrtk0VQFNQA02GPjXG/g9mQm9en/Miy\nwkLYw9ywm5khF9fnhpBlhf44souTAZ0ia2nUy/5ALIXTauJZRN9BMVJAyQr8w1qMo2yZC+N+Xp8K\nIgpwYTygC04FvZEkqAGw5XqTq7MhnZdQwGncXQp7HazHstyY03ZxQx4ba1E9CLu7fUzQZUUy+O7O\nhDw9l+h8J1S4S1weJM93K1euUarVsRl0ZKZDJ+aQ97ePNSClnxPUrZXdBK9Ph061AgC1w9hv2Nhf\n3eczGs+0+q6fa5E0y30kcF3+oqL0RniD3chu/em313n06BH37t1je3ubTCbzwtfoHzbTxUKhwPj4\nOL/0S7/Ez/zMz2Aymcjlcthsxp/RD7tegaGXWP1g5CyyxV42gfr+ZpTf+MzfGd5Xb6rHvTg9zMPd\nI40cfW1glDY55CZTaVBttJAVGPYZA5e5ET+Pdo9wnnKBvbsR4cKoh3qj1Qtw7NbDnWONo/VUyMuw\nz8m9zSj3tmI9NdhgPY8kubk4zpDXye31CJXOOKRYbWi4Q/1VLDf40QvTZIpVbq9HSHTa5Q+3j7Sy\n+E5tJUqa28eHPFxfnMBkkrh1fpJhn4u2rHCULbGyn8ZqNvFgM8ZeLEW1VIRaUVWQlUvUa1VoN1Hq\nZaxOF4LFjtnupqmI+PyBk85Xo4rN7aVRLVMqFVGaDVVRJkoo9RKKLNOWBRTA4XRBvYyiyJisVpqV\nIoLdA5KJar2GaHMhV4o4XB7azQZmkxmb00khn+Nof6f3upKFE8BpNYlsHBUAhcsTPi6Pe7m9k2Ll\nIEO9JeO2mTgs9IMBRec5M+gjc2HCR6ZcZ9ht5eK4jxuzQ5hEkcsTfuZDboJOC8ujPjbjeRKFKtFs\nmd1kAbMksnGUY+s4z068wF6ySKnSJF2q0VYUXFYToz47VpPA1ZkgN+dCXJkOMj/sxm3wWVwe8+uA\njM9h4clhWvfY+WEPrbaMoqhBqo/2UwRdNhwWk+653Ta94gwg6LKyephiZTeBLMtcm1M5MnazxFpU\nf0yAbKlGq62Oza73+QvNhLyGqiqPw8K3n0e5NDWke99DA8TzZKGKJKqEZSOpPagqssf7Kc4bkLSH\nvSfP15YVsqVqTz3Xbht3dw6SBYqnjNwA9pN5HAa8H1EQ2OmM1jaOMlyZPblGCAK9+3rn09e1NgqW\nfbQbJ+R1aDIT++swU6bmGObKlSt4PB5SqRQPHjxgZWWF/f19isXiP5oz86JxHGfRGVIUhU9+8pN8\n6lOf4vHjx/zCL/wCH//4xzk4OOiR0M+6XoGhl1iSJNFqtT60sZjR8V8WGErkyvybv/i2LsS0W5Fs\nmY8sjbEXzxqSOotVdWEc9bso17UdkwdbRyz07QbtFhOzYR9rh0ly5RqXdSMkta7MjVJtyYZdHlBJ\n3qIgcH1hjESuzEGin5za1o23vE4r58aCtBVFE9LYrYc7x1yaOiGYnhsPcnl2hGeHCRL5CvoIUHh+\nkNRlpA15HFjMJj5yfgqv0040VeT+Zow76xEyxRqZUlUzjru/dcTyQFRJs1JEsJzs+ARBoF6ro8gt\nmrUScr1MLpvF7faqXSCrC9ottdsDgIzcaoICfn+AUqUOoohSr1BrtRHMNmg1cDocCFYHcq2I2WZX\nF3JAdLgRBXA4HLSbdWr1JuVqhVbuiFYhxWTAoTFOXBr1sDTqZsLnYPUwi8Ukasaji2GvRl11cdxP\noY+I7TQLPI1k8NsklkI2rs8EsJslnBaJRKHG00iWcq3BdzfjrB5m2E4USJfqDG6knQau0dNDrv+P\nvTeNjS2/6z4/Z6l9r7LL++7ru+/XtzuEBAhNWhApICEkJAikyShCYdFMRnpEpBAkXjzhBSMYJkxa\nDxrNhIGQzJARMCFPMjQPIXQ66eu7797Xsst2uezaq846L065XKfOcdPddOcS1N939qnyOVWuOv/f\n//f7Lq3RmmlaZo0Bj8zrCzvcWckxs7TD3dUcpbrCvdUcA/Egl0asIulUX8wxFgLLF6hTLSaLMO/i\notwV8fOdpxl002R6Ik2y2e05OeBuNDjeE0Nri5G4vbTD6YEEV8a7HVwmgPF0zFak3FraYbgrSjrq\nzN86xFTT8+feyi6nB5LIhyJF3ENKN/crjHZHjh3FHfp53Vne5tqk/fu80+HBtVOoMpaO4pUl5jfd\neT+iaBHZ3TDSHWXnoMqTzJ6t2AFLbl9o6/btFCotSf9YOubgGs5t5jk33MVgKuIwmATQdJPxnhjr\ne+4eTV5Z4kv/7T6yLNPd3c3U1BTT09OcPn0ar9fL2toaN27c4OHDh2xublKrHa9Ae7up9YHAm1NN\nvpM4pJecOXOGP/7jP+bWrVu8+OKLfOhDH+JTn/oUH/vYxygW3d+zHxTeK4beIt4quSubzbK/v/8D\nGYt14t0iUGu6wW998f/ltcerx8rTI34P5bpKxSWBG2B1t8jzpwYxwCE5FQTwNjtnAa/MaE+Cp21K\nsDtLW62YjkNcOzHA/eUsK7kKF8ftPINDZPaKfOjiOLcWNh0ckeXsPtemjrozF8Z6kUSR24tb3F7Y\n4vyoewGWyZeY7I1xfqyX+cweD1a2QRCY39xzTbavNFQCMqSjQa6fHGJqoItcscr3nqyTL9UodwTT\nLmzu2cZlYPGZNvdKILbvdAVMtQHS0RhFMHUEUT76zAoC5XIJDAOzUaFer2OqatOxOgBag0g0wsHB\nAegqguxHkj0YSgNJ9hCMxCgcFDBNAckfwSeJmIcZQ2oNRJGaZmIKEuFwGEM3EbwBlOwcAcNa4CQB\nro4mETG5vZJveRF1jp8OOnb5crNzkQx5uTySZHoiTSzgZb+mMbtTY2lrn5mlXdvi7+lYKHpjAUcA\n6+n+uKNgSLkQl9u5WocY6Yqg6gaZ/Qp3V3LMLO4gSyJruRIne2NMj3dzsi+OTxZY2XHe6Ce7go7X\nCbRUVJWGyo3FbcoNlavj3ZRd+DqyKDi6FwBPMnn2SjXHGAwsCX4nFrMH9MQCrhJxsDtLP1jLMRj3\n4/dInBxIsuuiSAPrczqSjjo6SZIo2DzBbi9lOd3sEPUnQq7F1b2VXd431ec6OgSrcLm9tM3ZIWeH\nN912r9jIFW2O8akOl/jNfJnLzYKpK+JeNNQaastDyA0NRSMedB/ZjfXE+PaDVUdR5/f76evr4+zZ\ns1y/fp3R0VE0TWNubo4bN24wOzvLzs6OjW/0djpDpmm+5ee8UyiV7BvKj3zkI/zFX/wFd+/e5cqV\nKz+Qackb4b1i6F1CqVRibm4On8/H+fPnn8k/+t0ak/3h117l+083cOt8gMVv6YoEeLiW4/KE00wR\nrJ2hqhnsFNx3ok/Wd7g80cdIT5ynG3ZPIkXTGWnLO3v+1CA35zOt7kmuUHWEbUaDVpfnxtwG8WNU\nOo9XtxnqinG1qSpr9y7aLVQcLtnJSIDhdAyvLLaKoHbcms8w2nPkTyIKAhPpMH6/j5HeBDdmN5jL\n7HH4Ps41fYY6cWN2nYsdAbOqYRUakj+ELxhB8IWJRCMEg0FEX7gZzhpElmX8oVircDJNE0k0j/LL\nMEBTqdcVvD4/pbpGINzkVigVwuEIgXAUrVG1/HU81ntnKHV0E0RfENQakViccvEAJBlTqYKhg2lg\nqA0EycP9Wzc41eUlHfOzuFPkYVtS/FAqyFKbD9BQMshiG9F6Ih3GJ4uMdoXJVxrcXtljPmt1elqP\n6UvY/H/ifpGHHSOloVTINgISwEE6jge9POgYZ6VjfseIK+yTeewyslJVHU03mN06YGZxh9nNfc4N\nJumLB7k82kXYd/QZOqg5F/ahVJhHHV5BDU2noWksZg+YHk/bIivODaVsvj+HmOqL8zSzz83Fbc4O\nJlvKtIBXcngRHUIWRVZ3i1watRcUY91RljsKlJV8jdHuqMMa4RA+WeTpRp5H63tcGLVvmE72J9lv\n697qhsnmfomeWJCB1PEjnLqiHXv8sAO1V6wS6OAhldq6O7lijXPDR6+v4GIFMruZJ+z3UDmGLL6Y\nPXCN+jiELIqc6HOO/8AyhQT4P//p/rHPFwSBcDjM8PAwFy9e5Nq1a6TTacrlMvfv3+fWrVssLi5S\nr9ff0ub8WQeifuUrX+HrX/86y8vLVKtVdF1HVVUEQeC3f/u3aTQaPHjw4Jld33vF0DuMdrXYiRMn\nnqnB1btBoP7WrXm++Pc3Wj8/Wc85ukNXJvpZ3rUWs1yx6lBkyZLISDrOrcUtrk46OTRgEZaDXrnl\nUt2JWwubjPcmeO7UIK/PbtjOsZkv2cwRB1JRokEfTzdylGoKJ/rd+UG9ySjD6Ri3FpzBitn9MhfH\nrI6TKAhcPzmIomrcW97hcebAtXOkGSaCKJKMBLg42k0s6GFxt8xsJs+dxS3GXRQnrz9d42zbGFCW\nRKYGugn5vLz/zCiDyTBBn4dqUz4fCXhp1MqYSoVSsUi1bPFwyqUiZqOGVq9SrxQRPZY0XvL6ET0+\nIrGoNfpCwNQVwpEwSqMBSo1auYgQiCDIXgoH+6iaAaIHWWq686g1PIEQ9WoFQasjePwU8znLd6he\nQgzEqJRLCN4QgqYQDoUwdI27t2+SyRWZTNtJzZ1mhz3RAEPJINfGUvTG/CSCXl5f3GV5t4Rpwum+\nmC3FXRatmJJ2TPYm7MGuIo7i5dxQgq0Ofx+3cdZwKuxQIp12kdOf6I0xu9XZpTHJFevcX9vjzvIu\ndVXn7ECC959I24whD5GOBVxT6xVVR9EMZhazGLrO9EQav0eyBZm2o102/2jdys+6ONLF2cFUi/fW\njljQy6P1HA1N597Krs0c0c2sEGB1p0BDNVxJ0KcHU62u8K2lbabbRmF+lwLqoNIg6JcpVNy7TJIo\nMJfJ45clB4k74JWZbXKjsgcVzo0c3Y8iAa+jC3NnKUtXyEvY72HBxSqgWG1wdqjL7mjfBkHAGiMf\ng+xBmdlN94ihcpMO8Dffn6VwzDi/E6IokkgkGB8f5+rVq1y4cIFoNEqj0eD+/fvcvXuXtbU1yuXy\nmyp4npV03ePx8OUvf5kvfOEL/Nmf/Rlf/epX+drXvsbLL7/Mxz/+cT760Y9SKLhzzH4QeK8Yegdx\nqBY7HIuFw+Fnmhr/To/JVrb3+R//7L++4WOmpwa4MbfR+nl9t8ixM2/6AAAgAElEQVSZAfuif2m8\nj0dNB+r13YKjiyMKAmeH0rz2dIOrro7PFkbTcW7Mbrgee7y2Qzzs5/RQN6W6QmbvqNMwM7fBiX67\nEeL01CBrOwd89/EaZ4/xSboxu8Hzp4YYaZ633Gael90vEerINYuFfHRHgwwk/Nxb3W3FUIBVKCm6\n7rxhCgKiKPAjZ0Y4O5pGkgTmNnO89nSN7H6J7ULNtpgdHBwgeO0te0OptbLIWr9rVAiFguhKA6Va\noXhQsCT5AoQjYSqKcaRAE0RMpY4kgOQPoRsGgiBQKhYxBQFBtkjUoWgCwxQAAW8oiqnUrYJIqSAG\nYpiNEtFEinKxgBiIYtTLqHvrtsT69nT5iF9mejRJvtxgba/CzFKOrYMqmx0FS6cKbaonbBs3eSTB\nURydG0pSUezfhVrHSNIjCTaTQ3DnFMmi4JCrA46OBMD54S5Wc0efPU03eLSRZ7dUQzMMLo12cXog\nAZjEQ14erDm7Nid6Ysy2LdrlusrMQpbJnmiTZG1fANNRqyvbjmJN4d7KLgGv5Fq8TPUlWkWgaVrm\niFfH0/hlkblj/HlOD6a4v7rLWLM72o5Oe4wbC1mujKeRJfFY3k+loThsJtqvb79SZzF7wNUJ+xh8\nqj9hK2BvL2aZaHZkJ3vj6B0FgqabRHwSEz3OY4co1xtEjhl1jaZjPFjb5fyIkyKQigRYzxUpVBo2\nPiFYHaOlrPXaa4rG//XqY9e//6/B4/HQ3d2N3+9nenqaU6dOIcsyq6ur3Lhxg0ePHrG5uUm9/uaK\nrUN885vf5OTJk0xOTvIHf/AHjuPf/va3icViXLp0iUuXLvH7v//7b/q5AB//+Mf58pe/zIc//GHy\n+TyvvPIKr7zyCtVqlU9/+tO8+uqr/OiP/uhbezPeQTzbId0PIY6rqkulEg8ePGB4eLhFkn5WQamH\neCcJ1LWGwq//L3/nkIaD1R06M5zGMAxuLxzFVxzCUpdYWWHPnRzi9bYCZvugwvWOAurKZD83563u\nzEauiEeWUDuI2tNTA/zTgxUujPVyfznruKZyXeVDF8f5zoNlx65eECyVlMVNkjg/2svN+UzrWKHS\ncJzTI4lcPTHAbqHC2q6To7FbqDI9NcDMXIaAz8OF0R4erGS5MZexjPUGupjL2BeojVyB6alBZmY3\nGEhFGeyOsbVX5MHqNmeG0zxZ27F1CRazec4MJDs6HAKmUsXnD1hKsibMRgXBG7RGVs3XVavVEGQP\npqY2H1MlGotRPNyNmSbhaIxKQ8MrWITyWr0GhoHHF0AVLF5SMBxGEAKUCwUEXwCfBHXNRPQFMA2T\nSDSGaRhUiVCuNfCEomiajhiIIKsV5mdn8aSs78iZ/jg1VWMkFeLJ5gENzbCNyE73x3myefR+p8I+\nB++ns0NzYShBrthgMBlqLvwmkihwbjCBounUFZ2IX2YtVyLkETBN6/2Z6ouwuldjKBXCJ0t4ZZHe\nWJBiTUEQLIuGSkMlGfZxY2HHds7hVNgxXgOLX9KJqb6jDtKdFWtT0BMLcn4owa2lnMOnK+hzv01L\nosCtpW2m+hKohtEq0Ea7ow4SMlhhrf/yOMNIt+WzdGTSaLKx5xQI3Frc5gOn+rm55HSMB1qeQ483\n9jg33MXsZh5NN0mG/DxxGcXdW9nh/acG+OfH665/b6Qryo35La6M93B7yf7+titIby9mmeiNs9iM\nNemUseuGabkzv0EDZHmvyvu73UdZAEGfh+GuKLsu72NXNMhSdp9qw3kvHOqKkitaXcv1XLF13wOL\nLzTXpu77y39+yK/91CWkt0iCPoTR3KT4/X76+/vp7+/HNE3K5TL7+/s8ffoURVFQFIW1tTVeeOGF\nYwnXuq7zG7/xG/zDP/wDg4ODTE9P89GPfpQzZ87YHveBD3yAr3/962/ruYeE7xdffJEXX3wR0zSt\n4GjD+IFnaLrhvWLo3wjTNMlkMqytrXH+/HkbSfrfQzH0Tp3/P3/1O+wU3OWiAD6PxEq25Koc2ynW\nuXaiH8MweX12nc5iaT6zR8ArU1M0nms5S1twK5auTw1yY856zH6pZrvhHGJ6aoB/urfEaG+CZZd2\n9+JWnvefGWFzr+gYi2X2ijx3cpDvN72RhrtjyJLUKuLaj7Xj1nyGn7gwxp3FLVvBZ2JJ8QM+j21x\n9EgWp+uD50f5zoMVMm2+Oo/XdqzCseM8jzN5erribOeaBYIoIcleggE/imkt/AFZRNE0dN1A9Icw\ndZ2w30NZ0cAUCAeDVBsqfgnKpQqCJ2ARoAWBcqlEMBigWqnj9fsRfGHMRgVVqYPsIxKNUqla+WaC\nz49pgtpogOzD1FRCfh91RUXRTQTTIOT3UK7WEUQJQ1fxBryUS3tI/iBXTk0gSwIPN45ed+eIqrPj\nMN4dYaatszTVHUSWBKbHuqgpGjvFOnulhq0bc34owYN1ezfiwnCSYv2oiBKB9b0Ke2WFQzNorySQ\n3a+QbyN3iwLUGkFiAQ998RBhvwcTK5tqM19Ga6teT/XHXTPE3AJIK3WF1+ezNDSdq2Nd5Ep1VnNl\nBhJBHqw5R8UDyRAPVq3fz23tI4kC0+NplnaLPHXxCYIjQvnqbpGQz8Ol0W7uruxydrCLR+vu4+jt\nQpWBZJidQpVi20aoO+yxuVE/XMtxcaSbR+s5xntjzCy4KK0Mk7qiMZiKuBZfhwXck40922MEAZbb\n1G+aYdJQNHyyiGaYLLgo8pZ3Clw/0eewY2jHfrmKLIktJZ7tWvbLbORKDCQjZDqUpJVmdMfC1j7n\nRtI8avv/tBdm2f0yl8d7ubtsFZOdXMXMXolX7i7z4pWJY6/xX0Pn5lwQBCKRCJFIhOHhYQzD4OnT\np3zta1/jT/7kT9jd3eVzn/scL7zwAs8//zxer9WJu3HjBpOTk4yPjwPwi7/4i/zt3/6to6Bxw5t9\nriiKmKbJd7/7Xb75zW9am7NmPEckEuFzn/vc234f3gm8Nyb7N6BzLNapFnvWxdA7RaD+5s15/vwf\n7zLhwnEB6+Zerqv0p9xNzcBqTVuKMOd2bb9S58JYL9enBm1FxCGebORaCdXXTx4VQmDtvjp5R9eb\nHRoToaVK68SJgRRruwXXgFeA2wubDHbFuH5ykO2DCsttvkV3XIwhJ/uSjPYkebS64+hiAWzlS5xt\nyuGjQR/PnRwiEvRza2GLO4tb9CWdSsPXn65zro2L5PPITPbGqSoGnkAYSZbA1NHVGvsH+5im3swp\nK6E1aphaA0NtIAs6pXLJCmlVq5i6CmqdWq1qPUetI/jCBENhAsEg1bqC7PWiNOqYjTJ4A4QjUWTB\noKLomLqGaWCtUloNKRCCRpVgwEetWkHVTVDrIEhUSkUE2YtZL1vZZ4Ui0XAQJbvAYmaXu6tHO+W+\neICnbXEcyZC9CyRi0NB0ro13cWE4QTzowSMLPN4qMbO0y8ONfboiPlZ27YtXpxzdKjDsi+Sl0RS7\nZftOf7IraCuEAC6OdJHJVyhUFZ5u7nNzaYet/TKvzW4iiwKn+uNMj6c5O5hwTYqf6Im6egVZ7s4q\nimZwa2mH1d0iZwbinOh1T1PvjQVtv9cNk5nFbU70xBjvcX4PB5IhHrYVPJWGyt3lHa6NpzkmUoyR\n7gizm3nmt/aJh3w27lDKxT363qo1OtoruvvGhP0e7i5nMQ3D4aE01BVpqchqioYsCviaF3aiL+GQ\nsW/slbgwkm5GerjzdwrVhk051o7eqI/Ha7mWcqwd3dEAq7sFdNOweR6B1Ulu5xkpHarUTIdRaKHt\n2moumXRf+m/HE6nfCYiiyJkzZ/ijP/oj/uZv/oazZ89y8eJF/uqv/ornnnuOj3zkI6ytrZHJZBga\nOhJvDA4OkslkHH/vtdde48KFC/z0T/80jx5ZWWtv9rkAuVyOl156CY/Hw4ULFzh9+jRjY2O25z8r\nvFcMvUUcVuKHJoqpVOpYtdh/hGJoK19qGSveXdqyRV4c4spkP/OZPZtbaztS0SBruwfHcnEAdNNs\nkqWdxVKp2rDyvE4OOmI4AJ62FUtn+mPNYsn6O7MbOa505JZdHO9ldbvA+m6RE8eYLfo8MhN9SWbm\nMg4vJUUzCAcsPkHAK3N2IM5Sdp/l7X12i1WGu9wVL4tbeX7y4gQNVef12Y1WIVaqKYQCXmfHQBBo\nqDrvPzvCmeEeTNNkIVugVCqhKnVny1utE412FFWGjmaKCG2PrdZqTfJ06zSYag1NVajVqmDqeL1e\ni3ckStCooGgGmqoCAqFI1CqqVIVQOIpSLeENR6lWawTDETA0RF8ItDqiP4pZKyKFopj1Ep5AmMLB\nAYbkpbT+2CYV7o+HbGPBiZ4wQa/EpeEEl4aTXBvr5v7aHjeXdrm/lscrizzN2tWIZkeHcKo35gxg\n7SgkBOyGkGCpobJl++IlYrK27exC9ESDVtdD1Xma2WdmcRtNN3mcyXN6MMG1ie5Wcn3Q55Toh30y\nT13GSnulGt99muFEb8yWIJ+K+Lm/6uzkSILVEbm7vMvFkS6b43Vvx3t7iEy+RF3VXJ2qu9qKn9Xd\nIh5RpC8RQhIFNvbd+SgHlYbrPQLg5ECShmaQyZcZ7oranOj7OoxWV3YLLSJ0LODO3bm5uEVX9HjP\nnGjAa3sN7UgErPv17HqOaAc3aLjNqfrOcpaxNkXoZF/CNsac28xzZqjpfB8PstXh07SU3ef0YJdl\n7ujSoZ6Z3+Tx+q7j9+8GqtUqsViMn//5n+eLX/wid+7c4U//9E9Jp4+/L7fjypUrrK2tcf/+fX7r\nt36Ln/u5n3tb13DmzBl+7/d+j1/91V/lE5/4BJ/61Kd46aWX3vLfeqfxXjH0FtGuFrtw4QIDA+5q\nKHh2rP1D/FuLMd0w+B/+yzdaJoaKpjPZQTy+ONbbIjHPZvY42W8PKpUlkVQkQL5UY3Er75r+fGIg\nxf2lLCddPEIOISCw4uKnApb64/RwmutTgzzeLNJZUK3njlKnr58c5N5StlXg3JzPcGLA/pqGumPE\nwwG+83CVay6O0WAVWT95aZxIwMfjzYKNwvoks28LlfV7ZZ47OUhD1ZlZ2CQadN6gFzbzrQ5XyO/l\n2olBTg52M7+5x/Z+hfnNPfsIydAxRdkh5y+WSkfkaUFAlD1W694TRPAECARDiF4/Jga+ULQluRdM\nw+roNCX31WoVU9cRgVA4gqIb1jhNqVIpFRD8ESRZRlNVBF8IpVbFGwhSrlnqMlNXicVi6EqNeKob\nvV4lFI6iaSpIR+dQtpcwTdNGeo4FPVwbS1JtqFQbGndX89xd3bOFYgIMJ8O28eh4OmLjF4FzzJaO\n+rnfQVK+MJJkvWMRuzCcIl+2dxwujXazV7V3AnoiHu6uOBcz3TRQdYPHG3lmFnfY2C9zebQLv0dk\npNtesB52hToxkAyj6gbzWwc8Wt9jqjfO2cEk42n3/L6Lo91sN8nm91Z2MQyTy6PdRANeHrnwmQAG\nEmFmM3lkCcbSR0VAxO9x2AlsHVRoqBrXxrspuSjSwCrUbi5kHZligM1D69F6jqttfmDrOTfOUpar\n4z2sunD0DrFzUD6WU7W5V+JBW2p9Ow7f72JN4WSf/Z7V7jKNCaE29VvI7zzX4ZhtIOXuIycIMNoT\nO9Zz7c/f5e7QIdyiOEZHR/H7/QwMDLC+fjSS39jYcKxt0Wi05V79Mz/zM6iqSi6Xe1PPbYemaXz5\ny1/myZMnrKyskM1mqVSOp2D8oPBeMfQWUSgUbGqxf8/4t3aGXv77Gb73xM5Zube0RaI5++5LhFvq\niEMYHYXI5Ym+FmkwX6o5DBF74iH2ClUUzeDOwpZrFMfVyX6+P7vBQJd7/MUhNo5xfd0tVLk43meN\n2GY7/ZEENN1suU9fGOslX6yx0cxams3skegwZvPIEtenBvnek/WWQV47BEFgdeeAVDTItRMDhANe\nbsxlqCkapWqD7ljIYTcAlg3Bhy5OoGoGN+czrU7Zwlaei2NOvyatUUfwBJAkCdHrJxCKIPlDmJpK\nMBwF08TQNTRVwVSqeD0ytWoVQ2lgqgqNahnRY+2KPR6vVRjJPnzBMILsBV3BlLyWXb5ax1RrxBMJ\nq9hRqkiSB130cMhG93tlMA3M5osTBPB4vRQqdbzBMBVFR5BkRG8A0VARA1H0yj5aYZuzAwlGu0Oc\nG4xRqStN1dVBi/x+sjdqI1ZH/LIjgDXaMXoZ7Q63vIZkUaAr4mOqN85wKsyJnhin+uKc6Y8T8sqc\n7Isz2RNlpCvMQCLYNBI8KrRkUWBz33nD7o6F6Wy4nOqL2sJED1FTNG4sbLO6U2QwEeRcX4SxdMS1\nKzSQCHG/o8ia29pnM1+m3tBshQtYn+jtDtVdodrgzvIOV8fT+GSngiwW9PGwqercKVTZ2i9zccTa\nkJwcSFB3MTjcK9WpNTT6Y85uTcAjtV7LzPxWK+0erMDT2Q4u08zCFlfHe5jsjbO17+43VmkoeFyu\nHSz7hLlMnjODKcex4a5oi+uzfVC2KejiIR8bB0eF9Z3FLIPNQkYWBRY27f+Ph6u7nGwqYvdcDCZn\nM3ucGkh1ivpaeLS2y4DLGPwQ67m37rz8djyD3iiXbHp6mvn5eZaXl1EUha985St89KMftT0mm822\nznvjxg0MwyCVSr2p5x4+zzAMstksn/3sZ/mVX/kVfuEXfoEPfOADfPKTn2wdf1Z4j0D9FhGPxzl/\n/vyzvow3hX9LZ+jO4hb/0//zquP3DVXn4ngfdxY2Cfq9jpvY/GaeC2M93F/e5uxggpk5+1jr8fou\nIb+HSl0l6PPg93rYPrAWDlU3GO6OtbK8AM6NpLmzaBGcby9sMtGbcPh/WKTrDS6O9VrOzB0QBQHd\nMJryemcVspzd5/rUAIJAk7N09JhStcGVyT72m4TQoe4Ysii2eEv9cRk3rU0qEqQ3Gea7j9ccx56s\n73J9aqhJJofTQ93IkmXcuFuokIoE2dq3v46bC5kmcdzqwoVCIWoaGLoGsh+jUaWmtPETKmUEr99y\npW6iUasQDEeolo/+ttGoInhDqIeqM0CSA4imji4I+DwSDTGIoGuYWoNCoYjP56UhiPi8HsrVGhg6\ngjdAsXAAniCiWicUCnJwUEDwhTC1GoFgGEXVwQTB0AmEwlRrDfzhGB6lwM7uDpnq0d6s2OHB4+2Q\ng5/qizOzdFQsDCaD1BSNy6MpJFFAM0z8skhD0SjUFCoNDQG4sbBtG3NcHk3x2pxdjTg93m25SYsC\nsZCPaMDLSFeYck1lMBmmrmjky3VCfpmHHcRsAZMDFw7LucGkrdOyka+wAVyfsOTrXlni4VqOQ/ul\ndCzYpvY6wmRvnJmFrBUrM5ZmJVdkr1Tn0mg3d5Z3HI8P+mRuLWbxShKnB5K2ENapvjgzC0ehx3VF\n4/7qDtMTva4EZ4DR7gj3VnOEfBJj6ZjNjPHMUIpbi0ffhluL21wc7ebeyi6DqTCbeeeif39lh+em\n+l1J0GDxjFTV4hB1qkIPQ2lvLWY5PdBly2HrTYRaqs/tgwrTJ/qZWcg2X0OUu20cJM0wSIR8bOyV\nGO9NMLfh7PSZpkks6HN1+wZAMFnPHe+R80Zdh+kTx9uHHIe3G9IaCrk7Z8uyzBe+8AVefPFFdF3n\n137t1zh79iwvv/wyAL/+67/OX//1X/PFL34RWZYJBAJ85StfQRCEY5/bjsMpydjYGLdu3Wr9XlVV\nFEVpFUFv9TW9kxDeYoX5bC0s/x3ANE0U5fhAwE689tpr/MiP/Mi7eEXv/PkrdYX/7n/+G15zWcjB\nUo5dGu+1qb7aMdGXxDB01neLjhsYWMXLjbkNzo/0cH/FWUqMpGOs7hSY6EuyuVek1rZDPT3UzZO2\nGfthIXSIse5Iy/ARLHXHxbFebi9ucXGsl3suMnyPJHJ5oo/F7P4x5E+TcyM9+L0yD1e2HYTcU33R\nFvHXI0tcmehnZm4Dw4TpqX5HQQiWKul9p4bZLVZscluAsZ4EG7mCg6s0NdjN/G7Nksub7a18y43a\nVDp2rYKIKIlW5ljbY/FartFC80cwkbwB9Ebba292hg6JJoLHh2jqeLw+SxFnaKCrIMoIooSp1PAE\nwgi6gmII+CSThg6mUkXwBDCUKggiguS1HKsjYTRNo1pX8Eqg6ODrn0KQZKZ6Y8y1EakHEkE2Dyot\nzkvUL3Gy1/LmKVXr7JYajKQj3Fo+4tGMdYVZyZVsPJkro13cXj767FjdIj/ZNvl0LOhFa0roDxH2\nycii4IjOODOYoKbqJEM+TGC/VCcV8TPTIQsXMEmHPGx3cJC6Qh6KTdI0WCOmiZ44lYbCk419B3G6\nJxYkX6rZRmQBr8y54S72y3UWss6F+vpkDzfmrc+8KAhcnejh9tI2siQS9EqOGBSACyNdSKLI/dVd\nx/f36ngPtxatvxcNeklFgq2CaLIn5rgGrywx0RcnX6yy7SJTl0WBwVSYUk2xOYofHgv5ZAqVBtdP\n9HNj4ei7KwjQHfG3FGj9yTD5cr313Zzoidk2TbIk0peIsL5X4sJwytF1Azgz3E3Y77EJNNrx4+dH\n+KcHq67HBlIRgj6Pq4eSJApEfBKiKDuihwC+9N9/lB85/dYIxIqi8PjxYy5duvSmn/P3f//33Lt3\nj89//vNv6VzvBObn59ne3ub06dP83d/9Hb29vYRCIUKhEF6vl56enjfNXXobeFN8lffGZD8APGsb\n9LeKP/i//4Wii039ISZ6Exy8gVNorlAhFvS5FkIAD1ayPH9yyLUQAoiFAvQlI+yXarZCCKyuyoUx\nq/3upj6rq1pr5CVLIudHe7i9aO1+7y1nHU7RAZ+HqcEubsxnGD4mhd4jSUSCPh6t7boGZS7tlOhN\nhJkaSNEbD/P67EbL/fjB8jYDHSq74e4YZ4Z7mN/MOwiXAMvb+61xYioa5PlTQ/QlI8xncphqDW/n\n2EAQMJU6Hp+diyRIMqFAkGg0huANEAgGQfKAWiMei1o7G8F6vq7UkP1BPF4veHxWXIcngNcfAsmD\nqTYI+HzUKmXQGtbTfEFrLGbqFj9IVVAQkSQR1RQt/x5vCK9oIHqDCKKIB5VYNEKxVKZSriBIMrqm\nIAgiyvYipmm2VESHGEqGOD+Y4NpYitGuMCd748ws7TCztMvTbAlJgHurHXEZfo+tEBpMhrjXQTq+\nPNplK4TAMjjs5HacGkg4CqGLI1082siztF3g5tIOt5Z2yDZHTecGE0xPpBlLRxGAy2NpRyEEVmRI\nOw9sr1TnxkIWSRC4ONLl4BYNJEMOrlBN0VB1nUpd4eyQfVwU8ErMto0SDdNkZiHLeE+MaxM9roUQ\nQLWhcXtpm5P9CRsfJxr0tsxSAYpVhb1ilfGeGGNpZyEEFs/Q0+wwuuHMUBcr2wW6I0GHL9Dpwa5W\niOrNha1WfhlYCrN2L6XNfLllgpiOBR3dY003CPs9eGSRxWO6UNWG0vIIcoOuH38f70+EXU03wTKH\nPag0mOyLO45ZGzH3LMU3wtvJJavVasd2ht5t7O3tsbq6yt7eHi+//DJ/+Id/yKc//Wk+8YlP8MIL\nL7QKtPfGZP+BcTiqetYhdG8Wrz5e5c//8S6YJpP9SRY6djrRoJe13QKaYRIP+zlwSege6Um47oAO\ncWoojfYGH/rlbJ4T/alWEdOJ/XLN4XR9iK2DGpfHe3i4usuZ4TR3l+ydoL1itWWoGA/7SUWDPFqz\ndvJ3Frc4N5rm4crRzj4e9tMTD/G9p+tMnxhw7fJohsmpoW6+82CFzvqvruoEfDKSKBD0eTg9nObm\nXAbDtEYG1kjR2a3aL9X4yYsTfPvBkq3gE0wDUfKApmFb7UUBXRCtXDFDo1atYeoqpbJqOU3rOjXl\n8D0XOCgUj/yFAAQBrVEjHA6jlsutFrAqexFNAwORumYgeEOYhjUyQzWRPV58Xg8VRbNGdoIXv1ey\nvIUkCdMwkDwyUUmi0rAk4IVSxeIkiQZGvYzpCzTl/jrBxh6PNgT64kEGEgE03eDuaq5VhHokgUqH\n8WdXxMt2W1fhRG/M4SuUDPvY2DsqPMM+mbmOxXsgGXKQofsTQe6u2IuogEci48JxOTuYZGYxy0Zb\ngdsbDyJhcmmki9mtfWpNF+zx7jALLi7Wp/tjNqXYueEuFM2grmrcXXZ2MzySSDZfIXtQYWu/wqWx\nNOu5EnvlOueGulqjoXYs7xRQNZ1zw10Op+qTA8kW7+fR+h7jPTEKVYW9cp2TfUnbWA1oeQ+dH+lm\n+ZgRkiBY4/VkyE++I4LiUP33NLNnjbIWj663Pf/LME1yxSrRoJdiVSEWdEr7by1kmepPEA362Dlw\n/n+ebOT48XMjfPuY7k6pqjgK0HY8Xt/h3HB3i2fVDkXVeLCyw2BX1DFiTIb9LGKJJDyyaMXbNHF+\nNE3A61QY/mt4u2OyZxUP9fzzz/P8889TLBb5x3/8x2P5ts9yTPZeZ+gt4q0qxJ61vP6toFRr8J/+\nN0tGjyAQ9DlvOD3RAOWGRl3VOekiS79+cpD7K9us5Yqc7HN2WkbScR6v7XBvKetIngerpTzUHafs\n4u56iGQ46JBQt2Ntp8j5sR7XkdhmvsSViT76EmFCfg+L7VEDglUsHe5iR3vi+DxSK/doZi7DcNJ+\nM+mKBhlIBvj2gxWmp5wp9QALm/v8xMUJRFHixmzGVjDdX97mubZ0+4m+JBdGe1nM7vMvj1aZ6HOS\nQxuNBqLHjyiKCN4AgjeIJFoRGvV6HUVR7Y1hXUPyeDqUZwKmWkP0tpHDBYFy1RprHcLUFAzRgyiK\naI26NV4TBSSPl2gkjCFIaJqK1qiB7EMAyuUSgseL2agRD/mp1hQK5Sq6KRDwiJiyBxMBAUikUpiq\nAoaOPxBgf2OJpEdla7/CzaUcsiTaunEXh1Pstpku9sV8PMnaF5/ODsN4d4SFrQOSIR/9iSBj3RGu\njneTjgaY7Ikx2RNlIh1lJBUmGfYT8skcMgJSYb/DlO/ccMqR1D7SFebOsrPTOZgMM7O4zd2VHXRd\n5/xQkiujXfhk531EFgUHQffhWo65zbxF+nbpLFwa7Sbbxi4eMCgAACAASURBVLG7u7yDoulcn+w9\nNvbi4mg3yzsFHq7tNlVfRx9IqeP+trRtxeWMtPkAdcIEFjb3GHZRU6Uifh6t7bJ9U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blN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F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\nXJGF8W4iatBpeHGhvIF7fh6VCR1I+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i54kWwGDaFEa+YZwGk0JW3H/fidt0MVgqeHLr5H\nK96ToReEIAh4vV4WFhZwOC4a/M7jdZKh5/3aVoOGf/nf/7hksJztd0hN8Q1M9th4sB9g1RNmvLsd\ntVJBn910Qe2Z6G7uKJNxfz/IwqDYCdbAcKeFj5uSqDvMOg5DSYlkjrusPDgMgkw0gmaKFf56x8+K\nJ4zV0Mbf7AXYDyZRqxT89V6AdKnG6kmGdqOeWL7KkEPP7mkcg7JGLJ1ltMPIL352/InPvTH6TCaT\nlzbQvsnw+/3s7e2xuLj4SupinsWEnUqlXqoJO5PJ8OjRI8bHx6/U62fQabg1M0IskSKeyrLr9ZNI\n55ga7MJhNrJ+4EOo1lArFaiUcqlKIhRPIZOJ5ma7xUA8nWNuWNws2zg8kQIX5XWiUa3VpEBGQRBo\nb1qX94UTEiHZOQ61eIei8STj3TZW3QEK5QqjTapNMJ5mYeTMHBtJZluIlV6rRquSiwXPdRz5oy0b\nYsF4moV6dpHNpGPryM/WUfDCCrxK0fr2wkg32nMjtpog0GNvVW8b47Tz8EmKj7j95o2k8QTiUixB\nMxqK0U9+cD3HPc/ze5/L5d6ZG7erwHsy9IKQyWTMzs5+qhzZjDdNGWpgwGnmX3znK0z12luCDwE0\nKgWJbJFGBtCGN8KYy4KuTdWi9ujbVMQyZ48DsZbj+5sn7PkTLA934jTryBUrUnCiUi7DrGsjU+8t\nsurbiGQKNHpgb490suEV1/Xn+mzcPxDHbsvDHax5o7Qb2ohniygVcjRqBSZdGzazgeEuK+0WEza9\nhh/tV/HwwX12dnaIxWLSz6hcLrOyskJbWxvT09PvhFG6sT0VCARYWlp6Lb1qn2TC9nq9kgk7FLqo\nGrwI4vE46+vrzM7OYrFYnn7AJfFbv/iTpLN5up1Wuh1WaZvs0a4Xl92Kpk0lplLPjpAvlpgf6cHb\npA4NuUSCsncskohMvsjUgEhoHrtPpc2yR3teSR16tO9joONMHWrUe8CZOjTaZSGRLbW8zhtuv2RK\nBpHMNFON43AchVyGUiGnz2FhzRNqSbEOJjIMO1sJS6ONfqDDSjpXJJktMHfOJ7R+eEpXPZtIqZAT\njKXYPApeSJDe80Uks7RMBqeRJOtu/4WetNNoiqm6ajbd55SuIbYnhC1uHgVZHHExes7wfV1w2U0y\nOFutf49nw9t/db9meBOVoQaWR7v4zpcXL9yFzfU78cdbTbC6NjX5SgVnU5rsRHd7i6LUbtDglTbD\nZNw/CDLgtNBrN6Gr9xstDXewFxDN1zIZdFoNRNPinfNUj427dQWpu13PflAMWZzuaef+YRClQo7N\noCWaKTJeJ2c6tYqaIBJDg0bNb37tJp+7c5aVEwqFuHv3Lo8ePeKjjz6io6ODwcHBaxGN8LJRq9XY\n2tqiUCgwPz+PUnk9LIVPMmGnUinJhO31el+oyTsYDLK7u8vi4uJLu5N2Oe2MD7jwhyJEkxk2D31o\nVApGep30OKys7h/T32lj031KKp3FatShUioIx9PIZLCy58Vm1hNLZVkYEUnNY/eptO7eIAfNAYiC\nIGA1PVkdSmbzzPfb2D2Nk8jmyeTPEuFFonU26joOxVvUIX80xeJIN0ujPTz2+CmWK4ydyw8S5K2b\nd4f+KLdGu/h492wlOxRvHZ/XBIHeOolaGOnGF0mKW2wDraQpkT0zXM8NujiJpKhUa4x0X1R82lTi\nn7hC0xjtSdtr+WL52qpC8Hxk6P2Y7HJ4T4ZeMS670XWVeBFlCEQzrbUc5h/91A3JLjTmsl5Qigac\nZh4eBjkKpShXagw5jYx3mvj43PZYt81Iomm998ZQB/f2A9zbD6BQKPjhmV684bMZ//JIF1v1vCGH\nSctpTOw306jEwstcqUKnRYe3/v75PhsHwRSfGe8iX6yhVChQKRVEMkW0KgU/+8EI412iCtA8ppmY\nmCCbzWK32zk9PeXBgwd4PB4ymcwbmZXzLGg0sOt0umsdF9CchH379m1JsdvZ2eGjjz66oO49DcfH\nx/h8vleigv2Dv/0TxJJpHGY9I72dyJDhsBhZ2T3CYTZitxgIxlJMDLj4zw+3uTneT2e7iaXRPorl\nCsPdDXUoRJtKSTpXYHpQrLhYPzyRSldX9nxSZcfKvo/+Ju/QnalBbo71EI6nyTcJa3u+cAvp2K1/\njQZS5+pz9Bo197Y80ts73mDL4/dPWzvMtGqVtHLfgCcYuxB6uOEOYDFo8QbPug+jqYvbho3vp9hE\ncvzRi36gDU+QsW47200p18lsgemB1q+rkMv40RtjF46/LnjW9OlmPM1A/R6tuJ5XvDcMl1EN5HL5\na8tYeRFlKBKJsLKywszMDL/0pVv83s99FrVSQa5YpXnspZDLkMllVOpzrHi2QCpfok0pa3nc8khn\ni0G6y6qXiA5Am1LBQ3eYYDLHuMvK56Z6CCWzyGUyaXSWqKdkT3RbOY5m0KgUaFRKajWBD8c6EZCx\nOGDnr3cDWA1tBJN51CoFWrWSH53r5YemLnaINbwyN2/eZHJykuXlZebm5lCr1RwcHHD37t23rnqi\nUTDrcrkYGBh4o1SwJ5mwg8GgZMI+PT2lVLqYpi4IAvv7+8Tj8ZYAyZeJhYlBup02EuksIHDgC3Lv\n8QG3pocY7LazsuvFZbcQjCWRySCRyXJv000yk+P21CCBaJJ2k57oeXVIytkRyUi5WqXP2S49T5tJ\nz0RfBzfH+jgORHiw46VaE9jxhVta65trkuPpXEtH2cFpRPIZ3Rzv5S/W9plt6hpLZPIXmumbTdOz\nQ518vH8iKT8NFAqtW2TZQoml4W5pnR5EVWns3PbZ3kmYDyb72fKeJeIfhxNM9LV6vcqVKp3thvMZ\njFTPpVl/OD1Ah/Xle+OeF89Lht4rQ8+O66GDv0NQKpVvlDIkCAJHR0eEQiFu3rwpRbn/3GenUSjk\n/I//+i9aHn9zuFMaXTXgNOtYO0kw12/nKJzGpFOzenR2p6aQy9Br1PgT4qhDJhOVn+2TOCAjnCoQ\nShaI54poVAqWR5yk82VuDjkxatVkihVuDDnRKBW4I2k6LXruHYSxG7XkShWme2yseqMsDzvJFCt8\n/dYQP/vhyIXneXBwQCaTYWlpqWVEpFarcblcuFwuarUa8XiccDjM7u4uer0eh8OBzWZ7I83V6XSa\njY0NJicnX4pX5lWioe7Z7XYEQSCbzRIOh1lbW6NWq0kf0+v1bG9vo1QqmZ2dfaXk77/96S/y+//H\nn+Not9DvsqGQKcgVirSpVJj0WnqcVu5tulkc6+fRnpeJ/i62jwLotW0cBaP80MIYhVIVAQGbSUc0\nlePO1BAfbbpZPzxhtNeJxx8jnEhze3KAmiDgDcZQKRVs1wtM54e7WT08BWgxKD92+xnrdUpdYUfB\nqLSSD1CtVFkY6ebhzjEIwoVryWk0Ka3pA2y4T+nvsIkq0rYXBOhqN3McOovpOAwmcdnMUru9Vq3k\n4KT1+gFg0FzM/jpvwAZawl9BHB96/aELj9v0BrEZtUTrq/c/9eH0c42iXhWed0z23kD97Lier/xb\njOfJ+rkqXFYZalROZDKZFiLUwN/6gUn+6S99XroDHHSaeXDQOgq7MdzBZj1wcc0boU0tp99uotR0\nZ3ZjuIP9ui8I4NZIV50I1X1ClrNesjGXle9v+Vk5ipLMl/jLrVPuH4SQyWT89V6QTKFCKl9GIZej\nVSsxtKnIFsvM9tkoVmp8caaHn//MaMv3WK1WWV9fRxCEp3pl5HI5NptN2noaHBykUCiwurr6xo3T\nIpEIjx8/Zm5u7o0nQufRMGEPDg5KJmytVovH4+Ev/uIvyGQyWCyWV34ufvUHb6DXthFPpNGqVPhC\nMdb2vHj8IeZGeljZ82K3GKQ06sboqVAsgyBwf9vDpvuEu48PGXI5UCnl+GMJxrod9DgstBu1VKtV\n3KcRBEHg/paHYCyFvck0nGkKHlw9OJHGaCB6/RoIxtIsjJ6pQ21qJcViiZognruPPf6WzSxfOMH8\n8Jk6JAjQYdGTSOekXrANjx+jVt3ymF7H2e/e3JALTyglJc43sOY+bTFI9zgsfLTpQX9uRX/dHWip\nDRl0GnGH0i3VIQDVmsBwffXeoFXz+YVhqtUq5XKZSqVy7VTf98rQy8d7MvSK8aZskxWLRR48eIDR\naPzUTaqfvjPGv/jVL2PQqBCAahMJcJp17Jy01m0MOi381c4p0z3t9NmNTHa3S5UZABMuK/ebeseW\nRzqlQtZOi05sspfJMOvUxLMlqgIMd5hZ8USQyaDHZiCcLjDd004gkWOkw4zDrCVTrLA85OTv/vDE\nhef58ccfY7PZGB0dvZRKIJPJMBqNDA4OvnHjNJ/PJxWPvgu+ApVKhc1mo1gsMjExwfj4uGTCfvjw\n4QubsC+Dn/jsDXKFPMVSBafVyOxIL70ddj7ecrM01s9wt5N9X4jZ4W5W948ZdNnZ8QaYGugimy8y\nVR9X+UJxKpUaHn8Ui0mHLxTn3uYRvU4xUXn9wIelvuW14QlIPV4HJ2Fp5CUIAo6mfq/VgxP6nGeJ\nzKGYuEl2Y6yX9YMTNOpW8mE91z3WCGtsQIaMQtOYMlcoMXWuKmPD7cegUdPVbuLRnmiwNhpafyfL\nlSodpjOS02ExkCuWL3yuYrnCZNOorFhfS7UaL5KCxijux29PYTEZUavVKBQKZDIZ1WqVUqlEqVSi\nWq2+9nP4vTL08vGeDF0BLvMH9E3YJkulUjx48IChoSH6+/uf+vy+MNfPv/57P06m2Bp8ZjeJJKSB\nMZdVKlh97IuRzBUx69votYmzepNWTSxTlGT2ZqKkUsjRtanIFisi6Wk3EEkXMGnVpPIlKjWB5WEn\nmydxbg6J/oKpnnZ88SzH0Sw/9+EIf/8rrSORdDrNw4cPGRkZuZKiwcY4bX5+nlu3bmG326UQwbW1\ntU/0r7xKCILA3t4esVjsncpNyuVyPHz4kKGhIVwuFxaLhdHRUW7fvs3k5CQymUwyYe/u7l7KhH1Z\n/Hff+DKVapVKpUKpXKZarbG+f4xcLkcQBBRyGSaDlkpdPW03isRAUd/Q2vEGaFMpOY0kWBwTvUNu\nfwSlQjzeUW+PzxfLUlhqpVqTDNgAtdrZTcvKvk/yywiCgLPJO+MNxfn80hgPd71UazVW9324bCbp\n42v7PunrAWx7g5K/58ZYL3e3PIx2t/p4fJHWjrFsocT0QCdd7UZJMV4/vFjymshXkSGuxj/cE0Me\nw/HWZHwQFS2AgQ4L7oCoMO8cBy9skB0F44y67Pz0D4pdhHK5HJVKhVqtlv41Fl5et2r0PMpQPp9/\nrwxdAu/J0CvGdVeGAoEAGxsbLCwsYLc/e+bG4lAH/+63fpr5AfHCtzzS2VLC2qaUk86XW3yMgx0W\nPtoLcBzNMNtnZ2mwo55XJPaShVI5Gqbr+QEHhyHRV3BzqIPHvjgyGfTWlaDZXhv7gSQfjHRwEsui\nkMvYDSSp1AT+4U8u8q0PWj1CoVBIGhG1t7dz1Tg/ThsaGqJYLLK6usr9+/dxu92vfJzWPA6cnZ19\nruLRNxGpVIrV1VWmpqaemKSt1Wrp7e2VTNhWq1UyYb8MEqtWq1ieHqYqVFAqFFgMWga7HUwOdHF4\nEuLu4wMWR3s5OAkx0dfJyp5orF4/8DHc7SCezrFQzwyK1zetQvG09L7VPR8dVpGw7J9E0NbVnOag\nxk2PXwpXrFRrDHSdnQMreyI5Uirk3Jro4zgUk35Pa4JAj+NMOSpXawyfCzHUt6nptpslj9LhaaQl\nxfokkmRuuNVsXa5UebR3VrtRqdYY7W41TftjKWaHuhh2OaTNNE8oicvaqiJ5gnGGOq3YmwpYxQ2y\ni+WtvU4Ly+O9F94vl8tRKBSo1Wo0Gs0F1ahcLr9S1eh5lKFarXZt4jHeBLwnQ68Y11UZaigGJycn\nLC8vP9fopMtq4P/+Bz/BL31+hrUmgzTAYLuuJYvoxlAHK56zx7SpFPzFlg+1Ss7SkJOFAQcGjRq5\nTMZ8v13yIk12t3O//v9bwx2UqjXujHRQFQQEAQ7CKbRtKla9UW4MOviTv/MhX26q2RAEAY/Hw/Hx\nMTdu3HglI6Jm/8ry8jLz8/O0tbVJ47Tt7e2XPk4rlUo8evQIq9XK2NjYG7Ux9iKIRqNsbm4yPz+P\nyWR66uMVCgUOh4PJyUnJE9ZMYg8PD68kCfu3fvGnyGRy6DRtZPIFHGYjO94AyUyOhdE+Vve8DHc5\nsJn0VGs1euqjK7NevNM/CkZRyGUcnkaYq299BePizUK5WsVhEklPplCSPp49N6JqNiWv7vuk4MRy\ntcqwy85Yj4O7Wx52vEHGes7UnY3DkxZfzuNzZazb3iB2k45s3ZsUTmYukJ9K03VIIZeRyOQukJXD\n00hLkrX4WDkrB61dZT0dF29mNEpYPfe4htepGYsj3c90LpxXjVQqVYtqVCqVXqpq9DzK0HtcDu/J\n0BXgTRmTfZIy1MiYqdVqLC0tvdCacZtKyT/+5g/wv/43X5SSXmf77GyHzgLWOi06tk/PVKNem5GN\n+pp9tlhBqZDznzdPOIqk6W7XE88XGemycGPIiVIueoRuDTu5tx/EE04TThfYOonT3W4gX6qSL1b4\niaUB/uefu8Nc39lda61WY3Nzk1wu98rWqZ+E8+M0h8PR0sl11UpEY0TU399Pb+/Fu+C3FX6/n8PD\nQ5aWlp5rXHDeEzY/P49Wq+Xo6IiPPvqIzc1NQqHQc53PTpuFwe4OlEo5mVyBnaMTuu1m5kf7iCUz\nxNM5DPo21g99LE8M1EMXDazseel2WAlEkyyOiSS/XK/C8AZjzI+IVRl7J1HMevH8a4zQQBwXNUzZ\nK/s+yR9UKFUYr3tt5oe78fjDeENnWT/6JtNzrlhmuv8skyidK7Ss2c8Mdl7wFmXzrR1zjz0B+uqN\n9zfGejk8jV5omg8lMsydW9dXKxVY9K0J0tvekBQ62YBBr78QDrvhFstbG1DIZXzjc/NcFk9SjRoK\nTEM1KpfLV6oaXVYZehMWOK4b3pOhV4zrpgzlcjnu379PR0cH4+PjV6YY/OjCAP/vP/4GP3NnDF9U\nDEEEkMtkmPUasnUvkUohR6mQU6x7BYY6zDw8FFdhlXKZuBobznAQTJItlln3xUnkSuwGkgh11egw\nlOLWsJPHJ3Gmuq1850dm+Cd/6zZW/dnda7lc5tGjRxgMBiYnJ6/NCu35cdrw8PCVjtMSiYQ0InqW\n7ry3AQ31r1EpclW+KLVaTVdXF7Ozs9y+fZuuri6SySQPHjx4LhP2r/zMjxCLJehxWunvsqPTtJEv\nlvH4I8wO93AajpPO5hEEgekBF1MDXdRqgtQ/FqmXjm4d+Zmo13HEkqI6VCxXmKirQKF4Wsoliqdz\nzNfTpM/7g45DcW5P9bN6cMxJNNmSQr26fyIFOQIcnIZbRl/eYAy5TMbtyX7ub3vZ9ASk8RyIfWgj\n56ouOqwG2o06tjziOG3D7ZdM3g1Uq2dkwm7W83DX2zLSA7Ectt9xNhJTKeQc+iMt/Wsgdrc5DWe/\nC5+ZGaSz/elq4dPQUI3a2tok1ahx43lVqtHzKEOCILwzCvBV4Hr8RXiHcJ2UoVgsxqNHj5iamsLl\nuhhA+KJoN2j4o//6h/jffvmLDNvEO7KbIx3snJ7dcS4OOvGEzzJGCqWKFNi4NOTkoO4TWh7qYPs0\ngVwmw2HSksiVWOi38+AwxITLwv3DMH/rgxH+6c9/yLc+HJHKK0FMzv7444/p6+t7JkP468InjdMO\nDw/56KOPLj1OCwaD7OzssLCw8EwjorcBgiCwu7tLNptlfn7+pY0W5HI5Vqv1hUzYH8yN02m3UixX\nCEWT7B75QaixONaPUBPwhePM10dmx6Eoa3tePpwdZtcbxG4x4AlEJSVIrRKfpzeclDrLtj1+KUco\nVB+hgUh6GnEYq3s+uu1m7kwNkMpmEZq+38MmwlOt1aQgR4BwItNa0RFL8bn5ER5sHwENtaiVjJxX\ndDYO/Yx020nXVaNKtSatu0uP8fglw/ZQl41SpcpRIMb5M1ihPCNec0Muwoks+XMLHQD52tmRtwcs\n3Lt3j/39fRKJxJWoKS9LNbosGarVatf2Ondd8d5d9YpxXciQ1+vF7/dz48aNl15DcHvMxe98ZZCU\ntov//f9bl94/02vj3n5AOmknu608dEeaPhYEmYzJbiv3DoOAjJtDDu4dhOlu17MXSGAzahjptPD7\n37rDbO9Fc2w0GmV3d5eZmZlX0r5+lfi0sEedTofD4cBut19QPgRBwOv1Eo1GX3js+SahVquxsbGB\nTqd75b6ohgm7t7eXarVKLBaTyKher5cCH8+/Vl+4Ncv/85cf02k342w3I5PLKBTLbHlOGe52kiuU\nKFeqjLicfLR5SK1aBaHG/HAfK3vHUufW+sEJvU4rx+GEdCOQzOa5PTXI3S0P3mCMhdFeVvZ9+KNJ\nboz1cXgaZazPSZtSwV+u7QPgC8el4MRwIsON8X4+3vECYoiiQaOWcopi6TMVbLDLRjSZodq0pRaK\nt9ZjrB2eYDXopNLWYZf9Aqlx131CjU/TyCGq1gRW6mv3gViKmUEXG56zCI4dX5huu4WTSJJkVsxo\n2joK0mExEEycjeg9gRgjLjvJXJFf/sZXQKgRjUY5OTlha2sLg8GA3W6/shBVuVwuqdC1Wg1BEFqI\nULVaRS6XI5PJPlWtvuyY7P0m2eXxngxdAd4Uz5BMJkMQBDY3N6lUKty8efOVmfJkMhlfWRriy4uD\nrHjC/F/f3+JuExFaGHDw0B0GZNiMGo6jGZDJsOrbCKbygIyp7nbuHYRoUyqxGTV8YaaXr98aYrLn\nydtgPp8Pv9/P0tLShcDINw2NcZrNZmtJV15dXQXAbrfjcDjQ6XTs7u5SrVZZWFi4NuPAl41yucza\n2hpOp/O1+6IaJmyHw4EgCGQyGSKRiPRa2Ww2HA4HBoOBv/2Vz/Af/maFZLaIUqHg4DRMvljic4vj\npLJ5HuwcMdHXxab7BF2bGrc/QjqX597jQ5CBSiFjts+OP1mgo93McTjB+uEJwy4Hh6cRPH7Ri1Op\n1sgVSrSb9Ax12dGolWQLee4+PsSgbUOvUZMtlDiNJCXSBJDInBGebKHEnakB7m6J6s/haYTpwS5i\nqRzJbJ7D04j0dUEkHlMDXWzWt8pK5SqLow7ubh2ha1MRSWZIZVuvP6G64rRycCq9b+c4xFiPk2Ds\nbI1eRquqIgjQ4zBj1LVJW2w1QWCgq72FDAG0m/R88cZ43aMkp6Ojg46ODgRBIJ1OX3it7HY7RqPx\nhcl141xUKBQIgtBCjBojtcbjzpOjyypDuVwOrVb79Ae+h4T3ZOgV43WSoVKpRC6Xe60dVDKZjMVB\nJ4uDTgqlCvf2/Xx/y8f2SQKzro1UviRWcZyKidRdVj2bJ3GcJi2dFh2fnXRxe6SD26OdF3JDGmiM\nSorFIktLS2/dFkZjnNYYqZVKJSKRCAcHB0SjUfR6PcPDw6/723xlaCSADw4O4nQ6n37AK0TDhN0w\nYpfsWLfEAAAgAElEQVRKJaLRKG63m2w2i9lsZmbQxerhCUqFkiGXA4VCQTyVoa1NTafNhEajIpUr\ncHt6mLubh9yYGODjbQ83JkTVZnaom0gijEqh4IPpIaq1Gia9BofVCALMDncTiqcIJ9J0WPQ82HYD\nMDXoYtPtJ5MvSgoStDa8H5yEmezvYqtOMDyBGAq5TFKANGoVcrmMaFLcFG03ajlsev6N8V0Dh6cR\nFHIZM4Nd3KuTqsn+TraOzpLrm31CAAZtG5Vqa5jjljeIWa8l2VQgu38Soc/Zmlx9Gr6YQ7TnC/E/\n/d0ff+JrZTKZMJlMDA0NSa+V1+slnU5jMpmw2+20t7e/sNoqk8laCE+DEDX+Nfw+DWJ0WWUom82+\nE2GqV4n3ZOgV43WRoXQ6zfr6Omq1msHBwVf+9c9DEASUcvhgtJMPx7ok1SqczpPKlShWqpTKVYza\nNpwmLUat6pnIW6VSYX19HZPJ9M6skKvVamw2Gz6fj/HxcTQaDZFIhP39fbRa7SeO094GZDIZNjY2\nGB8fx2q1Pv2A14yGCburq4tarUYymeTLtyr81aMtMsUydouZk0gMfyRBR7uFib5O/nJtjx6nFW8g\nilwmI1lXazwnIeQyGY89p/Q4LfhCCfo727m36UapkGMzGQnGUwy57Lj9olrTaTsrSm2+mfAGY8hk\nosKyfRRgtMfJ3okYfdG8qRWIpbgx1sfDvWPsZj2RRJpmq83a4Slmg5ZkRhxVrR+c0mE1SmnP4USG\nH14Y5T+t7kvHaM9tnm14/LjazZzGRJ+T3ayjeC7ZulIVmOhxcrc+wgPQtikvXFuPwwnGep3sNrXW\nT/R1MOR6eoZa82slCAKpVIpIJMLR0RFyubyl6+4qVKPz47RmclQsFqX3NR7/aXg/Jrs83pOhK8Bl\nKxxe9dpjKBRif3+fubk51tbWXunXfhIEQaBSES9uzSe1TCbDadLhND3fSZzP51lfX6e3t5eurq6n\nH/CWIJPJsL6+zvj4uBQg2TxOi0QirK2tIQiCdAE3GAxvPFFMJBJsbW0xOzv7RtYONEzYVquVH1ja\n5/Ghj3AihRKBgQ4rep2Ge1uHfDAzTKVS496mm6XxfnGjymnBE0pIb7vsVnyhBJvuU3RtanLFEoNd\nNoLxlDjOGnKx6T5ldf+4XoyaZK3hMwrF8UeTLI728qg+HjPqznyEa4cn9Dgs+MKiWpvKFeiwGlHI\n5XgCMW5PDXISET9WLFdYHO3l7qYHEI3Xg53tEhkyaNvIFUo0M6h19yntRi2xemmqIECv08ppLMVY\nj4OVPZ94bTDrCSXPssqCiTNTOEBXu6klv6iB88btv/MjNy/9WslkMsxmM2azWdr4jEajHB4eSgpf\nQzV60aDD5nEawP7+PiqVCq1WK5G9p3mN3veSXR7vydArxqv8AyQIAoeHh8TjcZaXl6+FkbYxI2/I\nxFeFZDLJ5ubmW9G+fhnEYjF2d3efSAiax2kDAwMXRjRWq1W6gL9p3qJQKITb7WZxcfGlLwC8Cvzk\n55bZ8pzQplaj02opV2vsHwcQBIF4LI5MrsSk1xBPiv4Xk9EAoQSZ+ibW+sExRr2GVLbA7ekh7m66\neew5RdemIlcsS1thtZpAr7Od02gSQRDospk5rucJ5ZvGY2sHPjosRoKJNIIg4LKbJTJULFdw2UxS\nJcam5xStWiUd76krWI2U6G1vELVSQalSZbzXyd0tj2T2BjF9eqzXyUebR9LX3/WFUCvlUuiiIAg4\njJoWMuQJxOoKVgSHWc/K3jEyuQyTro1U7izXSPz6ckqVGk6LgS8tT77w69XW1tay3JBMJolEIrjd\nbpRKZYtq9LxoXL8LhQKzs7PSuOy8alSpVCRlqXEe53K592OyS+LNugJeY1y3u+xqtcrq6iqlUqll\no6hxQr0ONLI2rpoIBQIBtre3WVhYeKeI0OnpKfv7+ywuLj6TMtKQ/efm5rh9+zZOp5NoNMq9e/dY\nXV3l5OTktXenPQt8Ph9er5elpaW3gggBTI/00u2wom1TEU2kMes0dLRbmBvtI5GvsHkUYKjDQiCW\npN9hYv3QR4/Dwq43wHhfJ/limekBMR7juD7ySucKzA6Lq/drBydSjcb6oQ+jtk36v6munIjjseaK\njrPtzPV6lcfcUDexZBqa9sDSuSIzg2fRHIFYqiVxOpHJMzfczY2xXmkzzdU0rgPwBuMtb8fTOT4z\nO8y298xLFMkUL2yfWer1IkNdNsrVGqVyVQqPbCCVKzBTjxv41ueXLoQ7vijOxyxMT0+jUCjY29uT\nIjEikcil7BGCIHBwcEChUGB6elq6XjZW98/nGkHr6n46nX7jl0ZeNd6TobcQ+Xye+/fvY7fbLwQM\nXqa5/qogCAJyuZyTkxPK5fKVEaHGBaMREfCubE80nncoFOLGjRvPddGTy+W0t7czPj7O7du3GRkZ\nkTayGrUT6XT6WiXZNp53NBp9rQniLwtfvrOAgAxnu4lypcqgy8FxMIY/Gme8z4k7EMNuMdLb5UQQ\nwKwTPWCymjhy3veJZaSnkQTz9ZDF41DDCyTgqoc15golGs33+WK5JVyxeTy26fFLNRuFUoU7kwNs\nHJ6QyZdYPzhpKVINJ1rX6EuV1j/8pXKFnaOzVfgtb6DFi3QaTTIzePZ9qFUKcoXW1OpgPH0hSHHz\nKIDTYmDDfbZ9lmoyVTdQqdZQyGX83OdvXPjYVUOj0dDT08PCwoKUMB+NRrl//z6PHj3i+PiYfD7/\niccLgsD+/j6lUompqalPvV7K5XKUSuWFwMc/+7M/w+/3v4yn99biPRl6TXhZf2Ti8TgPHz5kfHyc\nnp6eCx9/1Qbuxvro1NQUpVKJtbU1Hjx4wNHR0aXSes+jWq2ysbFBpVJhYWHhnSkkrNVqPH78mHK5\nfGWhgjKZDL1ez8DAADdv3pRqJ9xu93Pf2V41arUaW1tblMtl5ubm3roNQYDPLU/TaTWgUas4DkVZ\n3fVQq9YY73FSKldIZAs4243c3zzkw9lhDvxxrAYdu74IDrOBSDLDiEv0jOXrRKKZGK0dnKlAR/6o\nVFdxcBKS1JK1pgZ7MTixG4fFwHR/J6v7x9L3Wq5WGWlqo/cEokz2d0hvP/b4pboNrVpFKpuny36m\nBqWyrRUeAMqm13RppIe7m24c5/yD51WdbKHEdH+H1IMG4ip+j71Vedo8CvC1H5ily/Zqw0cbkRjj\n4+PcuXOH8fFxBEFga2vrieGcjY7IcrksBXle5mvJZDJ+8zd/k+HhYf7sz/7sZT2ttxLvxl+Qa4aG\nifqqR2s+n4/j42OWlpY+USV5lcpQs1Far9czNDQktbdHIhF2d3cpFApS7orZbH6mn0mxWGRtbY2u\nrq4nEr63FQ3lxuFw0NfX9/QDnhPnN54SiQThcFjaTmv4IV6VDF+tVllbW8Nisby2SIhXAZlMxgdz\n4/y7v/yYgS47hVKFWqVMrlTh0B9lyOUkmclTKJWpVKoMuuw4zEb+cnWXoW4H4WSGQkW8ydrxBumx\nm/BF02TzolKSL5aZH+nl7uYhgViKpfpWWHO4YqVaY6DTRjCeRiYT63BK5YqkvCyMnGUQHZyICdWV\n+vVEc06p67Aa8QbjTPZ38PGul+WJ/paPZ871lW24T3FYDMhlMh7uHiEIMORyEE4dNT3Gj0WvJVEP\nVtRr1C1ZSA30OCz4Imdr9ZVqjZ/+7OV7yK4aOp2Ovr4++vr6pHDOUCjEzs6OZJBua2trGY09K2q1\nGr/+67+OTqfjT/7kT944H+DrhuK3f/u3L/P4Sz34XULD2PYs8Pv9dHR0XNndba1WY3t7m3Q6/dQu\nplAohMVieelr1tVqlWq1+sRtB6VSiclkorOzU/qDGwgEODg4IJUSN0Q0Gs0TT+Z0Os3q6iojIyN0\ndnZe+Pjbinw+z8rKCv39/S+lOuWTIJPJJALU3d2N0WgknU7j8Xg4OTmhWCyiVCpRq9UvhaSUSiVW\nVlbo6uqir6/vrSVCDfR22vlPDzao1QSOT8OEk1mcNit6rZp2k4H1Ax/j/Z0c+EIkMjli6SwLo30c\n1U3LwXiK6UEX4USGkd4O/NEUsVSWbpuRdL5EvlikXKlSEwSMOg3RlGhI1mnUxOuJ0qlsgfH+Doxa\nDSt7x4z3OqVtMJtJT7geYpgrllgY7cVfX4GPJDPYzQZJpYln8tya6Jfyi+LpHFq1WhqhRZNZBjpt\nErGpCQKzg13IahWCCfF7qVSr4vZZHbWawPxwNyd1orM02sPHu8d0thvJ5M8eV6nV6mRL/H0Z63Hw\nj37+S1f7Yr0g5HK5lE7e3d1NJBKhVCpRq9U4Pj6mUCggl8uf6dyqVqv8+q//OkajkT/+4z9+T4Ra\n8TvP8qD3ytBrQGNUdRWeh3K5zOrqKlarlYmJiaeeNC9bGWredHgWo7RCocDpdOJ0OhEEgWQySTgc\nxu12o1arpSTftrY2wuEwBwcHzM3NvVObEo1NuampKcxm89MPeElojNMaI7VyuSxt0GSzWSwWCw6H\nA6vVeiVEP5/PS8TXbn96LszbAItRz/RgN//hv6zQbjJgFABBoNvRzt9s7NNu0mHQasSgxHoIY7lS\nIZnJ8cHsKNvegDRuEkdeJoLxFJ32dk6iGaKpHBM9NnZOouweB6U8oYOTMNMDLtQqJYVSGa1Kxfr+\nSf27OjuHxfFXu2R4zhWbCEi1xpDLTqhOlka7HZIyDKIyNTfZw73tM6XHaTXgCcakt5OpNDu+qPR2\nMJ5mdsjFuvvM/xKsky+9Rs3Wkbhx1+9sJxA78y0FYqmWMMdf+vLt53o9XgUaIbFqtZqZmRlkMhmV\nSoVYLMbp6SlbW1ufWunSIEImk4k/+qM/ek+EnhPvydBrwFX5djKZDGtrawwPD9PR0fH0A67waz8J\nlyVC5yGTybBYLNJGWC6XIxwOs76+LhkOp6en36n8jAYBnJ+fv3bPW6VSfeI4TaPRSGGPzzNOS6fT\nbGxsvHYC+KpRKBToM7dh0GvJl2sYVCrSuSLr+17mxwdQKBQ82HLjtJo4CYuEJJHJkSuUeHzgI5xM\nY9Jp+MzcCKeRpESGVvePcVqMhBJpKsLZH0ulTGCow4JOo6ZNLZe2vQY6zzbJNg5PcNnNnNbVmM52\nk0SGto8CDLnsHPpFArNTX6Mf6LKx4/XTdW5rLHQuG2jLE0BTL2hWK+VEMwVmBrtayI/qHLH2BGOM\n9TppN+r4qJ5n1Mg5aoZeI5IGi0F7LUZkT4IgCGxvb6NQKBgdHZWumUqlsuUmsbnSRRAEHj9+zNDQ\nEB988AG/8Ru/gdVq5Q//8A/fE6EXwPuf3BXhVfeTNXqpZmdnn5kIwctThpp7dq5qdV6n09Hb24te\nr8disTA8PIzP55NMvU9rBX/TcXx8jNfr5caNG9eOCJ1H83banTt3GB0dpVwus76+zr179y61nRaN\nRnn8+DHz8/PvFBHK5XKsrKzwhR+8zfhADxq1Cp2mjVgqQ1+nvW4eFpABw91OfKEYcyO97B0HGevr\nIBBLMjfcy5bnlHKlwuFJiN1jP9MDncwMupgf7WF5cgCLUcdnF0bpbDeyexIhU6yw7gnycM+HRS8S\nV08gykSfeF2pCQK9jrN078fuU4loANjNZ7EO8XSOO1ODhGMpCqUKbn+UsZ4zo7XbH2Ws9+ztdL4o\nrb1P9TkJJTIola3kZ919ivlccKLVoJM6zwB84QRj9ViABraORKL1c1+4gUZ9/TYPG0ZqpVLZQoTO\no1HpMjg4yPLyspSt9b3vfY/p6Wnu3bvH8vIyyeTF6pH3eHa8V4ZeA16EDAmCgMfjIRwOs7y8fGnv\nz8tQhj4pUfpF0fhj2t7eTn9/PzKZrKXBvWE8NBgMOBwObDbbW7Fu3ZDNS6USi4uLb+Td3pPGaR6P\nh0wmg8VikcIez4/T/H6/tATwNtaHfBIaStjMzAxGo5HPL89w5A9TLJWYHHCRK5Y48AXJFUrcmBhg\ny3NKm0qJUL8ZMGjFlfhSWTwPNw5P0GvURJNZhrud3NtyYzXqyBZLlMpVlsb78UdFlWawy04wnqZW\nE5gYcPHRY7G7rFY5G4Ft1r9esVwhWyhxa3JA6hZbPzzBqGsjnSvispvJFYpSMz2A2dCaBWXStSqF\ngUiMgQ4rq4ciuVl3t1Z6lCtVJnqd3G0arynksgsVHeeTprOFErcm+vmFH11+5tfhVaFRmN3W1sbw\n8PClbh5VKhXf/OY3+f73v8/P/uzP8o1vfIN//+//Pf/sn/0zVCoV3/3ud/n617/+Er/7txOyS654\nX5/QkWuGSqXyzCRjZ2dHakO+DKrVKo8fP0ahUFzID3pWHBwcoNfrr8x8/LISpXO5HGtrawwNDX1q\n+WZDQg6FQkSj0ZbG8Dcxd6gRGdAoW33bDMONcVokEiEWi7WM0/x+P7FYjLm5uXcmKgHEOIydnR3m\n5uYkBbBWq/H3/uhfcngSRiaTse8LoVQoGex2ki0UUCiUGHUa7m+56e1oxx9NYjboiCYyDLjsePxR\nbk0NcW/TzWCXHXdA7Ca7OTnIg20PKoUCs1FHJJGh3aQnnStQrtZoN+nJZMX/KxVyrEY94Xrq9Xh3\nOzun4nisz2nFGzobTd2eGsQXjlOpVAjG0wx02iQvkEatQqVUkK6nQmvUStT18R+I6/Izgy4eNa3u\n354YaPEWDXbZcAfEz2cz6ckXikz0d0op2AAmnYZ8qUy5qej1mz+0yB9++2tX9EpdDRpjLq1Wy9DQ\n0KXP8Wq1yq/92q/hdDr5gz/4g5a/A6FQiHg8zvj4+FV/228ynukH/Obdcr4FeB51plAo8ODBAywW\nC9PT08+tFigUiisZLb2MsVgD8Xic1dVVpqamntpC3pCQh4eHuXXrlrSSurW1xd27d9nf3yeZTF6r\n8MBPQqlU4uHDh9jtdkZGRt46IgRn47SxsbGWcdrdu3fxeDyYzWZyudwb8XpdBcLhMLu7uywsLLSM\nQuVyOR/OjeOwmlCrlMyN9DIx2EWxXGLXG0AmE1CrlPVKDQvlSpWR+jjKaRGzdAJRkay4/REm66Oo\nRFrcHhNzgsSxUiyVlbKIYqksc/X/V6o1hrvPRk/lJq+RNxRn0Hk2wswXS5TLZWnrrKP9LM+nUCoz\n1d/Z9HaF8aZR2Y2xXlTK1utZONka4uj2Rxmpl6sOu2zkimUq59rtU7kC0+dCGX/hS7e4TmgmQs9z\ns1OtVvnud79LZ2fnBSIE4HQ63xOh58S7c/v1kvEyPUPJZJKNjQ0mJiaw2WxPP+BTIJfLX3hM1jBK\nN5cFXhVOT0/x+XzP3Tml0Wjo7e2lt7eXSqVCNBrl+PiYdDqN2WzG4XA8cTzzupHNZllfX2d0dPSF\nX+M3CVqtlnQ6TVdXF/39/USjUY6Ojp46Tnsb4Pf78fl8LXU5zfjq55b5j/fWyRdKFCsVtG1t7HhO\nGei0o9e0cW9jj9vTQ2Ivma6NvWMxgXrjwIdJp8EbjDEz1M3G4Sna+shx3xdirK+T3eMgez4xbLFS\nrZHOnSUiN/+/8TnL1RqHpxHG+zrZORY3tExGPYSSDHVY2Pf66bKZCNWP2/T4pbEaIJGkBrwBsUV+\nsr+Tu1seTDqN1F8GcOiPMuyyc3h6tlnWbtTRbTfzcOdY+ho2o45ouilnqIlD/8DMELODry6G4mlo\nBKY2Mtcui2q1yne+8x16enr4/d///TdyfH6d8f6n+RpwGTJ0enrK5uYmi4uLV/JH8kXJULMidJVE\nqJG8Gg6HuXHjxpV0TimVSjo6OpiZmeHOnTt0dXURj8e5f/8+Kysr16aLKx6Ps7a2xvT09DtFhCqV\nCo8ePcJsNjM6OiqFPc7OznL79m06OjpaXi+fz0exWHz6J34D4PV68fv9n0iEAPTaNuZG+zEbNCgU\ncrRtKuZG+nC2m1jb96LVtFEuV5gb6WN6sJtoMsPcaB+5YonJOgk4W7MXt8ngrHIjmswwNyKGlu54\ng5JStHMclBShaCrL3PBZsKlBe+bj2nD7+czMMN5wglypgl57ds6mcwXGus9+lz2BaIsaFEzkmB/u\nJpbKiJEa2fyFqg2buTU+Y+soQKfFKIU8Vqo1Rs6Zph83ma1/9aufeeLP9XWgVquxsbGBwWB4LiJU\nqVT41V/9VXp7e98ToZeE98rQa4BCoaBcLn/qYxrkIJPJsLy8fGUeCoVC8dwE4GUZpZt9MnNzcy9l\nPCSTybBarVit4lZMNpuVNvIA7HY7DocDvV7/SsdTgUAAr9f71rSvPyuKxSKrq6v09/c/cRuyMU5r\nbxfrJbLZLJFIhI2NDarVqpRabjQa36hxYqOJPJvNsrCw8NTz6Otf/IDvP9rCqNVQrdXQ69p4uH2E\nSqFgcsDFg61DLCYDvc52zHotyayokhwHoshksHZwLK3FD7kchBJp1vePaTfqiKVzLYGGVuPZmK7d\npOOgHjPUnBS9tn8ienbqo69KrSKNq7aOgtLnBVoqMgDaVK3P1WbSsdJc8XGuz6y57R7A5bBccH9E\n6plG0ueo1hjvcZAtlvnBueFP/dm+KtRqNdbX1zGbzQwMDFz6+AYRGhgY4Hd/93ffE6GXhPcJ1FeI\nZ/Xi5HI5isWidKE/j0qlwurqqhTLfpUjgnw+Tz6fv7QC8WmJ0i+CQqEgJQw3NsZeBdRqNRaLhe7u\nbhwOB6VSCZ/Ph8fjIZfLIZfLaWtre2nfT2MrMBKJsLCw8E5tTmWzWVZXVxkbG3vmJYLG6+VyuXA6\nnVQqFU5PT6WVffjk1PLrAkEQ2NnZoVKpPLPvz6jXsu0+IZXL4/GH8fojjPZ10WW3chyMksrlmRvu\n5cG2m8XRfhQKOSadFk8gyvxIH4FokunBbnzhOLliiUq1SrlaY36kF184QSSZYcjlIJ7OEUtl0Wnb\nKJYrRFNZ9Jr6/5MZhrrFx9QEgQ+mB8kVimx7A5TKFfLFMgLiCv7ccI+U+RPP5FsSpuPpHG1KBeWq\nwOKwi0d7PjRqpUR2IokMDstZgnWxXGFhpBt/NIVMJsNs0CBXyAk1jdzi6Rz9nTaS2bPRnq5NzXe+\n9lkpGuB1okGEGlUyl0WlUuHb3/42Q0ND/N7v/d61/v2+xnimBOr3P9nXgE8bk+VyOe7du0dXV9en\nZk88Ly6bM/QyjdKpVIpHjx4xOjr6SismzkOtVuNyuZifn2d5eRmr1Yrf7+fu3btsbGwQDAZbknRf\nFI3S0Xw+z/z8/Du1OZVIJFhbW2NmZkZS6S4LlUpFZ2enNE5rHn8+evQIn89HoXCxufx1ojEmUSqV\nly7g/PoXP6BUKjPk6mBySMwfKpXKnEYSzI30ceALopDLyJdKPNo5oqPdRJfNTLXWUGzEtfhmc/Th\naQSFXPwebPWcoGajc6FUZrKpzd5m0tNu0rM80c9j9wknEXGrLJRIMzvcLT3OVw+CbMDZZKQuVWrM\nDPUw2m1n7fCUfKlMr+0so6gmCAy5WslxsSxeJ2+M9bJ/EpZ8Qs3obDe2vF2qVPmJD6af6Wf7MlGr\n1VhbW8NqtdLf3//0A86hUqnwK7/yKwwPD/O7v/u7b5QC+ibi3bkKXyN8EhmKRqNsb28zMzPz0sLm\nLrNN9jKN0sFgEI/Hc+2SlZtX8wVBIJVKEQ6H8Xg8qFQq6WPPO9KqVCqsra21ZCe9KwiHwxweHl7p\nSFAul7eMPxup5Y8fP74247RG0WzjNb8spoZ6GOp2chSIEYwmiaUydNkszI70IggC4USaxfEBVve9\ndNrMfLSxj9moQ69Ri2v1/gjLk4Pc3/KQzokkMRRPsTjez6NdLxuHPkx6DalsAW8whkwGgoD0/3aj\nHqVCjlou4/6WmEE0N9LDWn2O1rz5dxJOMDXoYtMjJkhvuk8lAzZAplAknslTrYnHVGlVvQ99IUQX\ntPhabXr8DHS2c3gqRgM0fELRrbO1+8PTCDLOvNPf/anPvnYFpfGa2+12ent7L318pVLhl3/5lxkb\nG+N3fud33qnrxOvCe2XoNeA8GRIEgaOjI/b397l58+ZLTd19VgP1yzRKu91uTk5OWFpaulZE6Dxk\nMhlms5mRkRFu377N5OSktBp77949qVj2WdfAC4UCDx8+xOVyvdXt60+Cz+fj6OiIpaWll+qN0ul0\n9Pf3c+PGDRYXF9Hr9RwdHfHRRx+xublJOBx+aXU0T0K5XObRo0d0dHQ8FxFq4Bs/8iGVahmbWU9v\nhw2zQcf/z96bRrdZ3+nflyRLsi1rszYvsmx537fEWdgChdBCsEMhQAJlaQotFAZ4SqcHDp0Wpp1S\npqcz05Z2mE5nmPOfp6XzH3ACU0JCoU9apiXO6n23LNtabO2y9vV+Xsj37SWLbVmyJFufN22wLP8k\n2dJ1f5fr4rCYGFBpUSARwh8IIhwmoMwXwx8MoaxQhjMDE5DmctFcUYQsNhOsDAZGp+dQLo+0j3z+\nyNyixxegVu91JhsaSwvBymBAxOfgltYqzLs8+EvfBBRLIjroS/PKJnWQCRerM5nMxWtsp8eHhtJI\n5SibHaloCXMW/b9GNQYopIsVQoPdBaVs8d9hgkCxTADzgiUAABjnF/8/ABhtTtQuVLGKpMKER2+Q\nQkgikUQthJ544glUVVWlhdAmkq4MxYj1/MIubVWFw2EMDg6CIAi0tbXF/YpmLZUhUggRBBHT85CP\nNSMjY03Do8lGVlYWFAoFFAoFAoHAZWvg5Nr+lR4X6TBcU1NDZa9tB8iBYafTiZaWlk1dkSfbaXl5\neQiHw1QI8MTEBNhsNmX2GC9x5vP50N3dDaVSuapf1mrsqClFXq4AKp0RWWwWrE4XJjVGXNdUiUAo\njDP941DkiTE6Mwsmg47puchK+qBKC18gCF8giPrSQoBGQ75YCEFOFjw+P5rK5dSMTmulAiwmA1ks\nFlgZDPSNa9BUXkTN9Bhti7M6fSotxIIcmGxOhMJhlOSLqPX5PpUW/OxM2BeqUC6vDww6HRVyKXrG\nNdhVU7LsseWL+Jg2LLbXRHwuJucic0cKCR9Dk7plt5/QGlG8JCwWALIW4jaevvtGaoMuEYRCIUhK\n5i0AACAASURBVPT09EAqlUIul6/+DSsIBAJ44oknUFtbi+9+97tpIbSJpNan0RaBrAz5fD6cP38e\nOTk5qK+v3xRxsFplKBQKxWVjjDQU5PF4qK6uTjkhtJKVcysymQxmsxldXV3o6emBXq+nNgZNJhMG\nBgbQ2Ni4rYQQORvl9/vR2NiYUK8gsp1Gmj1WVVVRju7RVPlWw+12U/NwGxVCJIdu3QsGnYbsTBas\n8y6UFEgQCIaQwaCDzcpAvphPrdfrjFY0lMox7/ZSc0JZbBYGVFr8b/cIRqf0GFBpkcnMwPjMHLr6\nJ+APBHGmX4U/do+AkxWJzOhXaSFZWMlX6UyoXKgqhcJhlBcsrrWr9WbQFz64A8EQCpfMAo1Mz+G6\nOiV6xiNu0UNTs2AxF38XJrRG6nsBYECtByeTBTqNBhaLiTm7GxXy5bNEvMzl1/GDU7MoKxDj0L6W\njT3JG4AUQjKZLGoh9Pjjj6Ouri4thBJAujKUABgMBiWEqqqq1h3LsRGuNkC90cT5a+F0OtHf34/y\n8vJNfaybxdI1cIIgqLX97u5u+P1+hMNhNDY2gsPhrH5nW4RQKIS+vj7weDwolcqke2Mn22nFxcVU\nlW96ejom5pxkFbCurg48Hm/1b1gj+3bW4u2P/hdmuxO1ykJ4/QGoNHMwzzuxu74CfRMzyGQx4Vnw\nYmIwIhcc9oWcsN6JGXA5WXC4PGiqUKBrQIXBSR0yWUx4/QGwFgJSI+02EeYs8wiFwygrFFNVId6S\nFpdab6bmi+as82gsW5wjmvcsWofsqS1BYMkCgsPtxY5KBS6MRtbqTQt+R+T3enwBtFUXg06no2sw\nMqOUm8MBYKLuY9buxtLZIrfXj698YddCmO3mEwqFqK3YaJZBAoEAvvKVr6CxsRF/8zd/k3R/L9uB\n1L48T1FMJhMcDgeam5s3XRxcaXh76aB0rIWQ2WymAii3ohBaCY1GQ05ODkpKSiAQCJCdnY2SkhKo\nVCqcOXMGY2NjsNlsWzpugqwCSiSSqLKXNhuyyldfX09tp9lstqi202w2G1UFjKUQIrl//3Wwz7vg\ncHkwoNLA7fWhoawIJpsDlYp8NJQVYXBSh5I8EfrGZyAT8jA6M4eyQil8/iBqiyOzQWRUh8PtpbbB\neidmKKPDCc1itUatN4F8CftVWuQsVI1mLXbUKxc3yfz+RT8ijdGGupJ87K5V4szAJEZnDNT2GgDK\nmZqEseJ3xB8Mom9iMXdsZGYOGUuqyUabk3osACAX81AjZePMmTMYHh6GyWTatNmwYDCI7u5uFBQU\nbEgINTc3b1gIHT16FFKpFPX19Vf8OkEQePbZZ1FeXo7GxkZcvHgx6p+11UiLoRixll9ggiAwPj6O\n2dlZZGdnJ6RScKXh7XgMSgPAzMwMVCoVWltbkZOTs/o3bBHINWqCINDc3IyioiK0tLSgra0NfD4f\nWq0WZ86cwcDAAAwGw6YO9MYbj8eDixcvoqSkBIWFhat/Q5JBttMqKiqodhoZo0C2066WdWcymTAy\nMoLm5ua4/W1/rq0etWVFoAGoVxaitlQOgiAwOq2Hbd5JOUTLFlbrlQur6uT6vG7BA2hq1ozqhTV6\nMh0+GAqjYqENZlyyMj9rmaeGoCPD1osf+IwlAmVUY4JEEPk5NBoNBSIeugZUACKZZ+R9AJEtMZlw\nUSz2q3RU6jyNRkMwEIKQu/gc2pyey3LHsrMWnbu/9eDn0drSgt27d0MikcBsNi9zLo+X1cJSIZSf\nn7/6N6wgEAjg6NGjaGlpwcsvv7zh99/HHnsMJ0+evOrXP/zwQ4yNjWFsbAy//OUv8dRTT23o520l\n0m2yGEKj0a56xR8MBtHX14fs7Gy0trbis88+2+TTRVh6xngOSo+OjiIYDKK1tXVL5kpdDb/fj97e\nXshksss2SRgMBqRSKaRSaSSCYGGgV6VSUQO9EokEbDY7QaffGGR7qLa2Nq4bkZtJdnb2sqF5i8Wy\nLOtOLBZDJBLBYDBQmXrxNtB84Pbr8P1fvQtfMNIm6puYQZ6ID7GAi//vwhBubK7CpdFpZLGZmNBE\nKjL9Kg04mSxMz5lRqyzEkFpHVXhGp2ehLJRgUmeiBq8BRPpfC9CXVHVMSwap+1UaCLIzYXN7ESYI\nlBWIYXd5Ua/Mx5+6x8DNZlPp9EsJEwSU+bmYs84DiATHVilk6BpSY1d1MboGJ7G7VkkZOAJYVlkC\ngEH1LNjMDJQVitFxfcPCOekQiUSUqSzpXE5aLeTm5kIsFoPP529YeJBxMkVFRcjLy1v9G1bg9/tx\n9OhR7Ny5Ey+99FJMLkRvuukmqNXqq379vffewyOPPAIajYY9e/bAZrNBr9dHJeS2GmkxtAl4PB50\nd3ejuLg4oeaCwGIFa6mRYiyFUCAQQH9/P/h8PqqqqpK+RRJL3G43ent7UVZWBolEcs3b0mg0CAQC\nCAQCVFRUUP44fX19CIfDEIvFkEqlmx4PEi0WiwWjo6NbejaKyWRCJpNBJpMtE7MjIyMIhUJQKpXr\nMjSNlr2NlSiQCNE7PgO5VISKojwIeTkYUGmQycyAb2FVnkan4+yACi1VJbg0OoVdtaU4O6hCFjtS\nUemd0ICfkw270w0pn4tJnQk6kw31pXL0q7ToU2khy+VhzjKP/iXbYyqdCRVFUoxrDAiGwlBIBbCp\nZwEAJrsL5QViXByZBgA0VRTh7JAaQKTFtjSuY9pgWfa4DFYHFLJcXBqLfO9KA8f+ST24WWw4FuJB\nXF4/dlQW4a/uueWqfyMcDgccDgfFxcVUcLNWq8XQ0BC4XC4lZq+WD3c1AoEAuru7oVAorhgnsxqk\nEGpra8OLL764aX/jWq122UWaXC6HVqtNiyGk22Rxx2Kx4OLFi6ipqUm4EAIW54MCgUDM54PIFklB\nQUFKzIrEEpvNhp6eHtTW1q4qhK4EOdC7c+dOtLS0ICsri5ozGhkZgcVi2ZQP2miYnZ3F+Pg45euz\nHSA9qOh0Ovh8Ptra2kCj0TAwMICuri6Mj49ftZ0WC756z34UyUSg0YB8sQDjM7OR+aHyIvSrZjA0\nqYXX64csl4fAwnwOWdHpG5+BkJsNfyBItcoGJrWUSFo2SL3gLRQMhakgVwBUSwsAjPMRcVNXkg+r\n0wXakgqObUmifDAURsWSsFadyY6a4sWKisZohYSfDf+C67TWaENV0aLQ8AeCl0VsyHJ5+Fxr5Zqe\nMzK4ua6uDnv27EFRURFcLhcuXbqE8+fPQ61Ww+VyrfqakULoarl6q+H3+/HlL38Zu3bt2lQhlOba\npCtDcWRmZgZarTZmKewbhRRCeXl5uHDhAjIzM6nWzEZL+zabDUNDQ1uqRbJWSDft5uZmZGVlrf4N\nq8BkMpGfn4/8/HyEw2FYrVYYDAaMjIwgJycHEokkqqvZeDA1NQWz2YzW1tZtFStC5oyFw2E0NDSA\nRqOBw+FAoVBQFQiyncbj8ajXLFYt47a6MsilufhL7wgs8y7kiXJRlCeC3emB2+vH7rpydA1OoL5M\njiw2C3KpECqdEZWKPIxOz6JSkYeuARV0C7EaTo8PbbURl2pykNpsd0GliwxShwkCU7OL22O9E1pk\nsTLg8UdyzG5trcYnF4dBEASKZYvmjKMzc1DkiTA9F6kCzVnmlz0OTubi+05rhRwrk1j5nOXvm0tD\nY+k0Gp6+e19Uzx8pZvl8PsrKyuDz+WAymTA+Pg6Px0P5hgmFwmWVc9JEU6lURnXR4/f78dhjj2Hv\n3r341re+telCqLCwEDMzi+G4Go0mJWf74sH2effaBMh5nHA4jOHhYQQCAbS1tV31DZAgiE37Y1g6\nH1RSUgKlUrksuZ1Go1HCaL2u0Hq9HjMzM9sueZ0gCExPT1NiIB7iZOkMBEEQcDqdMBgMmJ6eXhYd\nEgsRth4IgsDY2Bj8fn9KGmhuBNI8lM1mX7EVTFYgVrbTJicnwWKxIBaLNxTpQvLskTug0hogEnCR\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NsbGxMTgcDjQ1NW16CCidTkdOTg5kMhkKCwtBp9NhMBgwMTFBpX9nZmbG7YPKaDRidHQU\nTU1N2271lZyVUCqV6zKSpNFoYLFYEAqFKCwshEgkgsfjwfT0NKampuDxeMBgMK65tp9oyJwxJpN5\nxZyxVKVCkQ+13ghmBgMagwUOlwf1ZUUYnZ6FWMCD3eVGdUkBJvUmlBWIYHF4IBdxYZx3w+XxIRAM\nIRgKo6lcAa3RCpPdCamQD5fHB48vsLgyHyYoYeVweUEAEHA5yBfxYHd5rrhyb3W4wcpgILDgTVSS\nJ4Juoc0WCIXQVC6H3mxHcV4u/u3FR8BmxqdK53K50Nvbi/r6+qiEkNvtxpEjR3DPPffgqaee2jK/\nO1uQNa3Wp/YlUAqz3spQPNtiwWAQPT09YDAYSbE1RWYD1dTUYM+ePSgqKoLD4cCFCxdw6dIlaDQa\n+Hy+1e9ojczMzGB6eho7duzYdiuvDoeDWiPeaEuUzWZDLpejpaUFbW1t4PP50Gq1OHPmDAYGBmAw\nGGJuJ7ERyLZgTk7OloyU+bunHgCfkw2twYIaZQGm9BHTzQwGHXqTDQGfDxWFIuRJIhdkc3Y3GHQa\nrA43SvMj/21mLtLGCocJKPMj7TGz3UkNT+tMNtSWRAS0PxjCvqZK+Hx+XBiegoS/6MQ/qV9sh3l8\nAdSULIru4elZsJZUi/yBINjMDPzzCw+Bmx2fAfalQiiaix+3243Dhw/j3nvvxZNPPrnlfne2I6nb\nGE9C4jUzFM9BaY/Hg76+vqSNlyC3nMhNJ7fbDaPRiL6+PhAEQQ1gR+MDQ1bDfD4fWlpaUr49sl4s\nFgtGR0fj4qPDYDAglUohlUqXeeOoVCqw2WzqdUuUb1Osc8aSkaxMFl4+ejdU2jlwstgYmtShrqwI\n/SoNuNlsjE7PgaDRMKm34LqGcticbijyRLg0Or1wUWCGzmRHkVSAGaMdE5o56r6XvgfxOVnYU1eK\nYbUecxY7nAuVonGNgRqWnrPMo6akAENqPQDA519suzncXrRUKnBpYQV/UK3Ha1/7IupjlEi/EqfT\nib6+PjQ0NKwpOmklpBC677778NWvfjUthLYI2+vdP4lYqxiKZ0XIbrdTLqvJKISuRHZ2NoqLi7Fz\n506qnTc2NoYzZ85gbGwMNpttTQPYZFWATqejvr5+2wmhubk5jI+Po6WlJe6GguRGYUVFBfbs2YPK\nykoq7Pbs2bOYnJyE0+nctMF5MnizqKhoywohkgpFPr7xpbswoNIgJ4uNLDYT/kAQCqkQHn8A9aVy\nBEORC61BlRYZdDp215WCTqOhcGHIOl8cqRIZ7S6UF4iRycyA1TaP1go5qhUy9I5No2dsGjanG4Nq\nHXIX5oxMdidVNQIAbtai8B1U65HLW/y9W/raH76tDYdva4vL87FRIeRyufDAAw/g/vvvTwuhLUa6\nMpQg1iKG4jkoPTs7i6mpqZR2FmaxWFRYbCgUgtlshlarxdDQEPh8PmX0uFLo+P1+9PT0oKCgYMt/\nGF6J6elpmEwmtLa2JmRrisPhgMPhoLi4GH6/H2azGSqVCi6XC7m5uZBIJBAIBHERqInIGUs0d+/b\nidEpPT7rHUXv2DSy2Ez4QhHx4fFF/L7I1fju0alIhpjDjT11ZTDPO2C0zaNCLoXX74csl49xnQlT\nc1YIedkYnpoFANSV5GFgao7yHCIzyTKXDEMPTempFf1QOIxyuQRnByMO0wMqHficLNSXFuJ7j3fE\n5XlwOBzo7++PuhLqcrlw+PBhHD58GI8//nhaCG0x0mIoQawmhpZWg2L5oUAQBCYnJ2G327Fjx46U\nXiFeytK2DJnabjAYMDY2Bg6HQyWA+/1+9PX1oaKi4rIU6q0OQRAYHx+H1+tFc3NzUlTDWCwW8vPz\nkZ+fj3A4DKvVCoPBgJGREeTk5FDxILEY6CerAtGuUKcy3/zSATz7ug7nBoPYVVmGs4MqlBRIMDip\nhSyXB7XeiHK5DOMaAyoV+egamMCcdR4eXwAqrQE7qkswOjMLk92JLFYGPL4AXN7FVlcovFjZ0RkX\nXaUHVTpksZnw+AJwuL1orVTg4mikHWZakj0WCIVwfUMZfvjUPciIw8xiLITQAw88gIcepvo4lQAA\nIABJREFUeghf+cpXYn6+NIkn8e+GW4hYzAzFsy0WCoXQ399PuSpvFSG0EjqdDqFQSK1/K5VKeDwe\nnDt3Dl1dXRCJRAnNmkoEpKM2QRBJ2xYkB+erq6uxZ88eFBcXw+Vy4dKlS7hw4QKmp6fh8Xiium8y\nbLaxsXHbCSGCIDA0NIQnD96EXXVlsC8YJ+blRjyAlPmRwXmRIDJIbLJFNsAmdUaUFkS+RqbSuxcC\nW4FIDplCFqmujWmMlFP1jNGO/NzIfbl9fpTlL150hJeIpgmtEYqFlfsCMR/ffvTAisyz2DA/P4+B\ngQE0NTVF9XfvdDpjJoROnjyJqqoqlJeX44c//OFlX7fb7Whvb0dTUxPq6urw1ltvbejnpVk7yfeO\nuE24khiK56C03+/HxYsXIRAIUFVVlZQfhvGARqOBy+UiOzsbGRkZ2LFjBzIzMzEwMICzZ89S2WNb\nOWYiGAyiu7sbXC4XlZWVKVHep9Fo4PF4KCsru6JB5/j4OGW5sBpmsxlDQ0NRfximMuFwGH19fcjK\nykJdTTX+45WnkMlmQSETYXR6Fgw6DTNzkUrO6JQeGQw6JjQGyj9IIoysnA+oNNQskHeJwWbBwlxR\nKBxGReGiN1dx/uJmYjC4+D7XP6mlAmEBID+XD4mAi7df+Srk0vWHoq6G3W7H4OAgGhsbo9oUJYXQ\nl770pQ0LoVAohKeffhoffvghBgcH8fbbb2NwcHDZbX7+85+jtrYWPT09OH36NF544YWkjy7aKmyP\nT8RNZK0fNHQ6fdkbeTwrQk6nExcvXkRpaSmKiopidr+pANkW1Ov1aG1tBZ/PR1FREXbs2IGWlhZk\nZWVhcnISZ86cwcjIyKYbPcYbn8+HixcvoqCgAMXFxYk+TtSsNOjkcrmYmZnBmTNnMDg4CKPReMVK\n69zcHGUimqqzcdFCLgnw+XzKSJPHycKvv/cMWqpKYJl3omHBR6imOB9Whwv1ZZH3h7zcSPVsXDMH\nOo0WmQVS5AGIJN6LF6pI6iUr8wbrPPX/p2YX//uY1gTRgiFjMBSGQrzo6WO0zuP/fPvLUBYsmjfG\nCrvdTongjQihRx55BEePHt3wec6ePYvy8nKUlpaCxWLh8OHDeO+995bdhkajURdnTqcTubm5W7aC\nn2ykn+UkIJ6D0mT6dkNDw7a8Kh4eHgYANDU1XVYNYzKZy+ZVLBYLZmdnMTIyAi6XC6lUCpFIlHDf\npWhxu93o7e3dcsPCGRkZkMlkkMlk1HyY0WjExMQEsrKyqPkwg8GAubm5hA2KJ5JQKISenh5IpVLI\n5fJlXxNws/G9p+7D9JyZuiDLySaFYuTfpAgy251oLC9C7/gMzAszPqFwGGVyKUw2B2bNdtQqCzGo\n1kGlM6KkQAK13gS92Y6a4nwMTc0uDEvLYF4Yqg4Qkfc3uUSAVx+5DS6TFhess9TrFguvL5vNhuHh\nYTQ1NUUlgp1OJ+6//3489thjeOyxxzZ8HgDQarXLLkblcjm6urqW3eaZZ55BR0cHCgoK4HA48F//\n9V/bpoqfaLbXO0QSEs9BaTJ0srW1FSwWK2b3nQoEg0H09vYiNzcXxcXFqwpMOp0OsVgMsVgMgiAw\nPz8Pg8EAlUqFzMxMyhcnVZ5Hsj0QralcqkDOhwmFQhAEAbfbDYPBgK6uLoRCISgUCvh8vm0lhkgP\npcLCwqtaZuTycvB/X3sWz/34/2BKb8LQpBaZLCYGVBoIcrJhsjnQUK5A38QMmBmRi4FxzRxK8sVQ\nz5phsCwGs+ZkLf5N5OXyqGrRUsNEs31xWHpkeha3tFbjx391PyQLFSav1wuTyYSRkRH4fD6IRCKI\nxWIIBIJ1XxySQqi5uRmZmes3bXQ4HHjggQdw9OhRPPLII+v+/o1w6tQpNDc34w9/+AMmJiawf/9+\n3HjjjVE5ZKdZH2nJGWPW+odLzgf5fL6YV4PIiojD4diWQsjr9VKtoZKSknU/t6TRI+mLU1FRQX3A\nnD9/Hmq1Oqnzt0wmE4aGhtDc3LylhdBKaDQasrOzEQgEkJubiz179oDNZlM+VKOjo7BarVuqDboS\n0kNJoVCs6h2WxWbhzReP4pEDN8Lp8aKutBCBYAhVC1lhrAURFDFpjIiKPFFkRkilM0K5MFw9pNZT\nDtIqrQHkn9vwlJ66j3GNAcULw9b37GvFm3/9MCWEgEgbdKV7uV6vx5kzZ9Df34/Z2dk1hQFbrdYN\nC6H7778/LkKosLAQMzMz1L81Gs1l1h5vvfUW7rnnHtBoNJSXl0OpVFLV7TTxhbbOwdGtO2UaIwKB\nwKpvtqQQmpmZgU6nA5PJhEQigVQq3bAjbyAQQF9f35orIlsNcoW2uroaQmHsBzJ9Ph+MRiOMRiN8\nPh/EYjEkEgl4PF5SPNc6nQ5arRZNTU3bTgSHw2EMDQ2ByWReFq8RCoVgsVhgNBpht9vB5XKptf2t\nUjXy+Xzo7u5GWVkZxOL1zeB8fLYP/3LsD/isb5xasWezMsBiMuFwe7GrthRnB1WQCnkw2h0gCGBP\nXRm6BlQAgNaqElwcnQIA1JfK0T+pBQC0VBTj0lgksf6Gxgq039CMB2/fveZzkVVak8kEs9kMBoNB\n/c2tbKeRjuotLS1RvY/Oz8/j/vvvxxNPPIGHH3543d+/GsFgEJWVlfjkk09QWFiItrY2/OY3v0Fd\nXR11m6eeegoymQyvvPIK1eLt6elZ9+uZZhlremNOi6EYs5oYutJ8kMfjgcFggNFopCImpFLpunvn\n5IxIaWnptktdBzZ/PioYDMJsNsNoNMLhcEAgEEAqlUIoFG56n58gCKjVathsNjQ2NqbsnFO0kI7W\nfD5/1Wog+QFrNBphNpupixGJRBJVNSEZiIWZ5KzZhpf/+f/i1Jk+lORHZn921UU8iSJRGjoAQH2Z\nHP0qLcQCLqx2F8IEgaaKIvSMawAAbTVKnBtWAwCaKxToHpvBjU0V+P5X70Fp4cby78h2GnkxQpp0\nhsNhjI+Po7m5OWohdN999+FrX/savvSlL23ojNfixIkTeP755xEKhXD06FG8/PLLePPNNwEATz75\nJHQ6HR577DHo9XoQBIEXX3wxrufZJqTFUCK4lhhay6C03++nhJHf74dYLIZUKkVOTs413+DJ8nBd\nXd227C9rNBro9fqEVUTC4TBsNhsMBgOsVis4HA6kUinEYnHcKw8EQWBkZAThcBjV1dXbbuCSDBqW\nyWSXDQuvBY/HQ1X7QqEQRCLRmv7mkgXyIqi6uhoCgWDD9/dp9zDePvUZ3v/0UkQETelBo9GQL+JD\nZ7JhZ40S5xfETkOZHP0TWmQw6OBysmB1uMHJYiMUJuD1B1BeKMX/c/h2dNzYsuFzrYSs9mk0Glgs\nFojFYshksnWbdJJC6Mknn8RDDz0U83OmSThpMZQIgsHgFVd8yUFpAGv+sAoGgzCZTDAYDFRUgVQq\nvWyoUKfTQaPRoLGxMWWvbKOFIAhMTEzA5XKhvr4+KSoi5FqswWCAyWSKa+WBNNLMycmh1qe3E36/\nH93d3SguLoZMJtvw/QUCAara53Q6IRQKIZFIElLtWwukq3asB+XD4TA+PjeA//jdnzCuMUBnsmFP\nfRnO9E8gm80CQYukz++sVuLCgjDaXVdKxXB8cV8r9u+qx517G8FgxO95M5lMmJiYQHNzM9XCXq2d\nthS73Y777rsPX//61/Hggw/G7ZxpEkpaDCWClWIoVkaK4XCYepO22+3g8/mQSCSwWq3weDxJIwQ2\nE9JVmc1mXzYjkkysrDyQwojD4WzozORQd15eXlQVkVSHbA3FK1qFrPYZjUZYLJZlsS6xiAfZKKSz\ncrSho2tletaE0xeH0TM+gz9dGsacxY7WqhKcH1Yji80Eg0aHgMvBDU2VqCrOxxf2NKBIFn8rB5PJ\nBJVKhebm5suqwVdrp/H5fErUkkLo6aefxpEjR+J+3jQJIy2GEsFSMRQvR2mCIGCxWDA0NIRgMEhV\njDajJZMskEJAJpOllJFkIBCghJHH41kWTLqe3w+v14uenh4olcptOR+22TljBEHA5XJR1T46nU6J\n2lj44qwXcn08WmfljeAPBDFnsSNMEGAyGODlZCMna2OLH+vFaDRicnISLS0tqwrTpcPzP//5z6HT\n6XDrrbfi2LFjeO6553D48OFNOnWaBJEWQ4kgFAohGAzG1UjR6/Wit7cXcrkc+fn5cDgcMBgMMJvN\nYLFYkEqlKeWJs17IGYmysjJIJBsbyEwkKzeceDwepFIpcnNzr1nlI4VATU1NTGZEUg3SQyneFZFr\nsXKrUCQSUZWHeFcoya2paNfHUx2DwQC1Wr0mIbSScDiMjz/+GK+//jrMZjOKiopw4MABtLe3o6Ki\nIk4nTpNg0mIoEYRCIQQCgbgJIbI0frXVcdJ0zmg0gkajUZtpWyWKwGazYWhoaMsNihMEAbvdDoPB\nAIvFssxJeamotVqtGBkZ2ZaO4kAkZ2xsbCxqZ+F4EAqFqBb2/Pw8eDwetbYf69a10WikWkMbteFI\nRQwGA6amptDc3BxVq9Jms+HQoUN4/vnncf/990On0+GDDz7A//zP/4DFYuGdd96Jw6nTJJi0GEoE\nfX19yMvLQ1ZWVswHLufm5jA5Obnm0rjP56OEUTAYpDbTNjqrkijm5uagVqvR2NiYNB+E8YBsyRiN\nRphMJkrU0ul06PX6bTkoD0Ref/KDMFmrnqSoJQd52Ww21U7bqHiZm5vD9PR01EIg1dno47darTh0\n6BC+8Y1v4L777rvs6+FwOCmH5NNsmLQYSgSvv/46fv3rX6OiogIdHR34/Oc/v+EKBukhY7Va0dDQ\nENUbQSAQoDbTyFkVqVS6KWX9jUIQBKanp2E2m6N+/KmM1+vF6OgoLBbLsmgQLpeb9K9drNBoNJib\nm0NjY2NKvf4ul4sa5A2Hw1EPz+t0Ouh0OjQ3N2+bucClzM7OQqPRRP34SSH0wgsv4NChQ3E4YZok\nJi2GEkU4HEZ3dzfeffddnDp1ChKJBO3t7Thw4ADEYvG63gTD4TAGBwfBYDBQVVUVkysXsqxvMBgS\nbha4GqSHTigUQk1NTdKdL96Q1gFutxv19fUIh8PUh2sqrH7HAtJMsqGhIaU3Jv1+P9VOI60yyOH5\na712MzMzMBqNaGpqSunHHy16vR5arXbDQuib3/wm7r333jicME2SkxZDyQD5Yd7Z2Ynf/e53YLFY\nOHDgADo6OiCXy68pjPx+P3p7eyGVSqFQKOJyvpVmgWRMgVgsTvgbL+kqzOPxoFQqt00VhISMl8jI\nyEBlZeVljz8cDsNqtcJoNMJqtSInJwdSqXTLREwQBIGxsTH4/X7U1tZuKbEXDoep4XmbzYacnBxq\nzmhp5WtqagpWqxWNjY1b6vGvFZ1OR5mpRvM7bbFYcOjQIXzrW9/CPffcE4cTpkkB0mIo2SAIAhqN\nBseOHcPx48fhcrlw5513oqOj47IPO61Wi5mZGZSXl29aLs3StHaz2YzMzExqM22zWxM+nw89PT2Q\ny+UoKCjY1J+dDASDQfT19UEoFKKkpGTV2xMEcdlWYaxmVRLBakJwK0G+disNAz0eD/x+P+rr67e1\nEGpubo7qwsxiseDee+/Fiy++iC9+8YtxOGGaFCEthpIdo9GI999/H8eOHYNOp8Ntt92GgwcPQq1W\n49VXX8WpU6di4qobLaSvitFoBIPBoDbT4j2863Q60d/fv6GcpVTG7/dTQnC15PGr4Xa7qdVvgiCW\nDc8nO6SrNo/HWzVnbCvi8XgwODgIl8sFNptNre0nSxjwZqDVajE3Nxd1a9BsNuPQoUNpIZQGSIuh\n1GJ+fh4nTpzAj370I8zNzeHAgQO49957sWfPnqRoeXi9XkoYkS7K8fhwJT1U6uvrE+Yhk0hID6VY\nuir7/X5qeN7r9W6qJ8562WjOWKpDEASGh4dBo9FQVVW1bG3f4XBQzvOreVGlMhqNBgaDYcNC6KWX\nXsLdd98dhxOmSTHSYiiVCAaDeOGFF2A2m/HGG2/gf//3f/Huu+/i3Llz2LVrFzo6OrBv376kaHms\n/HAlM4A2euWq0+mg1WrR2NiYFI9zsyE9pOLpobTSEyeZPlzJnDGFQoG8vLyEniURkMsSbDYb5eXl\nV5wRI9f2r+VFlcrMzMzAZDKhsbExaiF077334tvf/jY6OjricMI0KUhaDKUKBEHgi1/8Inbu3ImX\nX3552ZtgMBjEp59+is7OTpw+fRq1tbXo6OjA/v37k6JyEgqFKGFEbjeRYbJrnXMgCAIqlQoOhyPl\nN4aiJRFmguSHK2n0mJ2dTcW6bPaMmNfrRXd396bOyCUT4XAY/f394HK5UCqVq96eIAjKYNVkMgHA\nsrX9VIS0z2hqaopqRspkMuHQoUNpIZRmJWkxlEqo1epVB2XD4TDOnz+Pzs5OnDp1CnK5HHfddRcO\nHDiQFLM15HaTwWCAzWZbkxMveTWckZGBqqqqpGvbbAZ6vR4ajQZNTU0Ju8Jfmb1FzohJJJK4izOX\ny4W+vj5UV1dvy3iRUCiE3t5eiESiqLdG/X4/NSPm9XqjzrxLFNPT07BYLFFvzRmNRhw6dAjf+c53\n0N7eHocTpklh0mJoK0MQBAYHB9HZ2YkPPvgA2dnZaG9vR0dHB/Ly8hL+BnileImVVYdAIIDe3l6I\nxWIUFxcn9LyJgCCIZavTyVQR83q9MBqNMBgMCIVCEIlEkEqlyMnJienvVjLkjCWSeMxIrcy8I+0y\nktVyYWpqivKR2ogQ+u53v4u77rorDidMk+KkxdB2gXSoPnbsGN577z0EAgEqfLCsrCwphNHSzTQm\nkwmBQIC5uTmUlZVty9T1VDKTJN3L12sWuBrksHwy5YxtJoFAAN3d3RvaGlwN0i6DXNtnMplUxS8Z\nIl3UajXm5+ejtg8wGo2499578eqrr+LAgQNxOGGaLUBaDG1HCIKAwWDA8ePHcfz4cRiNRtx+++3o\n6OhIGr8Sg8GAoaEhsNnsZSv7a8lb2wqEQiEMDAwgOzs7KcTqeiDNAg0GA1V1II0e11PZIpPHm5qa\ntuWwPDksXlJSsqkXAx6Ph2qnxbPitxYmJyfhcDiifl8yGAw4dOgQ/vZv/xZ33nnnhs9z8uRJPPfc\ncwiFQnj88cfx4osvXnab06dP4/nnn0cgEIBYLMYf//jHDf/cNHEnLYbSRFKaf/e73+H48eMYGxvD\nLbfcgvb2duzatSshbRmj0YiJiQkqbNbv91MVI7/fT/nhJOLNeTMgW4NSqRRFRUWJPs6GWGnSyWaz\nKZPOa80+abVaylU4lXLGYoXP50N3dzfKysoSOiweCASozcLNjnZRqVRwuVyoq6vbkBD63ve+hzvu\nuGPD5wmFQqisrMTvf/97yOVytLW14e2330ZtbS11G5vNhuuuuw4nT56EQqGAwWDYllXtFCQthtIs\nx+1246OPPkJnZycuXryIvXv3oqOjAzfeeOOmDO7OzMxQRmpX+hAMBoPUZhrZjiE307aCMPJ6vejp\n6YFSqdySb6Iul4uqOgC4YsWPDBxOthmpzcLj8aCnpwdVVVUQCoWJPg7FymgXDodDre3HWrBOTEzA\n4/Ggrq4uqr/rubk5HDp0CH/3d3+HL3zhCzE502effYZXXnkFp06dAgC89tprAICXXnqJus0vfvEL\n6HQ6fP/734/Jz0yzaaTFUJqrEwgEcPr0aXR2duLTTz9FY2MjOjo6cNttt8W8XUVmTPl8vjVfCYbD\nYeqq1W63U344IpEoKVp964V01d4uG1M+n48SRj6fDyKRCD6fDwRBRF0NSHXIrbmamhrw+fxEH+eq\nEAQBp9MJo9EIk8kEOp1OzRlt5L2BDB32+Xyora1NGiEEAO+88w5OnjyJX/3qVwCA//zP/0RXVxfe\neOMN6jZke2xgYAAOhwPPPfccHnnkkZidIU3cWNMvWvKtFqTZFJhMJvbv34/9+/cjFArhzJkzOHbs\nGF577TUolUq0t7fjjjvu2PAHNxmtwOFwUF9fv+Y3wKVvwARBUGGy4+Pj4HA41GZaMm7HrMRms2F4\neHhbuWqz2WzI5XLI5XKqNej1ekGn0zEyMkIZPW4XUeR0OtHX14f6+npwudxEH+ea0Gg0cLlccLlc\nlJaWUsJ2ZGSEErbrdTAnCALj4+NU6G40Qmh2dhaHDh3Ca6+9hs9//vPr/v6NEgwGceHCBXzyySfw\neDzYu3cv9uzZg8rKyk0/S5rYk/yfJGniDoPBwPXXX4/rr7+eMn979913cfDgQQiFQrS3t+PAgQOQ\nyWTrehMjM7by8/M3tDZMo9EgFAohFAqpq9a5uTlMTU2BxWKtaU4lURgMBkxOTqK5uTkptnc2G9JH\nSigUQqlULhO2Y2NjlLBdmda+lSCdxRsbG1PSEHGpsCUdzLVaLYaGhtbkJUYKoUAgsGEh9MMf/hC3\n3377Rh/SZRQWFmJmZob6t0ajQWFh4bLbyOVyiEQicDgccDgc3HTTTejp6UmLoS1Cuk2W5qqQZe3O\nzk68//77oNFouPPOO9HR0bFqgCbZEohlxtaVIF14jUYjaDQaNaeSDKvaMzMzMBgMaGxs3LIf9Nci\nGAyit7cXEonkisPipLAlB7AzMjKSau07FpBVwa1oH0B6iZFr++QAvVgspjYECYLA6OgowuEwqqur\nNySEXn/9dezfvz/WDwNA5He1srISn3zyCQoLC9HW1obf/OY3qKuro24zNDSEZ555BqdOnYLf78eu\nXbvw29/+FvX19XE5U5qYkZ4ZShM7CIKAXq/HsWPHcPz4cdhsNtxxxx3o6OhAdXX1snbH6OgozGbz\nprcEfD4fJYyCweCypPbNHMAmRaTb7UZdXd22HBQmq4Lr8dBZufadqNcvVpARK9ulKkgO0JtMJhAE\nAZFIBJfLhYyMjA0Lob//+7/HbbfdFodTL3LixAk8//zzCIVCOHr0KF5++WW8+eabAIAnn3wSAPCj\nH/0Ib731Fuh0Oh5//HE8//zzcT1TmpiQFkNp4ofFYsH777+P48ePQ61W49Zbb0VHRwd6enrwy1/+\nEp988klCZyNIo0CDwQCPx0NtpsU7qT0cDmNoaAgMBmPbxouQW3MbWR0PBAKUMCJfv1SKlzAajVR7\nNBnbt/HG5/Ohv78fHo8HDAYjKqNOvV6P++67Dz/60Y9w6623xvnEabYwaTGUZnNwOp348MMP8YMf\n/ABWqxX79+/HPffcg+uuuy4p2kMrk9oFAgGkUmnM/VTIjCmhUIji4uKU+NCONfHIGVsZL7GWOZVE\nMjc3h+npaTQ3NyfF7/9mQxAEhoeHwWAwUFFRAYIgqNfPZrMhJyeHev2u9vykhVCaGJIWQ8nAaq6m\nBEHgueeew4kTJ5CdnY3/+I//QGtra4JOGx3BYBBPP/00aDQa/uEf/gF/+tOf0NnZib/85S9obW1F\ne3s7Pve5zyXFzEQ4HKYGeK1WK5XbJBaLN/TBSraFCgsLUVBQEMMTpw7koHA826NXyrwjX79kqMDo\ndDrodDo0NzenxKZjrCEIAkNDQ2AymSgvL7/sgoAgCDgcDmrOiHSgFwgE4PF4ACLP4X333Ycf//jH\n+NznPpeIh5Fma5EWQ4lmLa6mJ06cwM9+9jOcOHECXV1deO6559DV1ZXAU68PgiBw8OBB3HDDDfjr\nv/7rZW9+oVAIf/7zn9HZ2Yk//OEPqKioQHt7O77whS9Qb3yJZKWDcmZmJrWZtp4retJIL97D4skM\nmTNGOotvBmTmHTmnkugB+pmZGRiNRjQ1NSVlxSrekOHRbDZ7zTEzZCDwT37yE/zhD3/A3r17cfbs\nWfz0pz9NV4TSxIq0GEo0a3E1/drXvoabb74ZR44cAQBUVVXh9OnTcQtujAcqlQqlpaXXvE04HEZ3\ndzc6Oztx8uRJiMVidHR04MCBAxCLxUnRUloaJrs0M+1aw69kNaSuri4pBF4iSJacMa/XS82JBQIB\nKneLy+XG/fdLrVbDbrdHnbye6kQjhFYyODiI559/HtnZ2ZidncV1112HgwcP4pZbbtkWA+hp4kba\ndDHRaLXaZSvFcrn8sqrPlW6j1WpTSgytJoSAiIlia2srWltb8b3vfQ+jo6Po7OzEkSNHwGKxcODA\nAXR0dEAulydMGHE4HCiVSiiVSni9XhgMBgwMDCAUClHCaKlPDLkt1NTUtG1CZldCtoVaWloSPh+T\nmZlJ+eGQ0S5TU1Nxzd0iCAIqlQput3tbC6GBgQFkZWWhrKwsqvvQaDR44okn8E//9E/Yt28fgsEg\n/vznP+P999+nKudp0sSTtBhKs+nQaDRUVVXhpZdewosvvgiNRoNjx47hqaeegtvtxh133IH29vaE\nbmNlZmZCoVBAoVDA7/fDZDJhbGwMXq8XYrEYdDodJpMJra2tSTGrkgimpqZgsVjQ0tKSdG2hjIwM\n5OXlIS8vb1nu1ujoKHJyciijx43M9ZAxM8FgcF3u6luJcDiMgYEBcDicNV0UXQmNRoP7778fP/nJ\nT7Bv3z4Akddv37591L/TpIk3aTEUR9biarqW22xlaDQaioqK8Oyzz+LZZ5+F0WjE+++/j+985zvQ\n6XS47bbb0NHRgebm5oRddbNYLBQUFKCgoAChUAiDg4OwWq3IyMiASqWiwmS3S1WA9FHyeDxoampK\n+sdNp9MhEokgEomoAV6ytcdkMqk5sfW0+MiNKTqdjpqamm0rhPr7+8HlcqFUKqO6j5mZGTzwwAP4\n6U9/iptuuinGJ0yTZu2kZ4biyFpcTT/44AO88cYb1AD1s88+i7Nnzybw1MnD/Pw8Tpw4gWPHjmFw\ncBD79u1De3s79u7dm5BNHdJNl4wVAACr1QqDwQCbzZb0K9+xgNwWotPpW8JHye12U35GBEEsM3q8\nGmTESGZmZtTzMalOOBxGX18f+Hw+SkpKoroPUgj97Gc/w4033hjbA6ZJs0h6gDoZWM3VlCAIPPPM\nMzh58iSys7Px1ltvYefOnQk+dfLh9Xrx8ccfo7OzE2fPnsWuXbvQ3t6Om2++eVOPa7YFAAAgAElE\nQVSGdsmr4Ozs7Ct+AF5p5ZuMJkj0LE2sIJ8DsiWy1UQA2Q41GAzwer1XDCQlRQCPx4u6GpLqkM+B\nQCBAcXFxVPcxPT2Nw4cP44033sANN9wQ4xOmSbOMtBhKszUJBoP49NNP0dnZidOnT6OmpgYHDx7E\n/v3745IKT6auS6XSK2ZsrYRc+TYYDDCZTFTmllQqTei21UYgc8bEYjEUCkWijxN3Vhp18vl8iEQi\naLXabfMcXIlwOIze3l7k5uZG/RyQQujnP/85rr/++hifME2ay0iLoTRbn3A4jAsXLuDdd9/FRx99\nhIKCArS3t+POO++MieeP1+tFb28viouLIZPJoroPj8dDrewTBEEJo1TZQAsEAuju7l5XzthWgiAI\nmM1mDA0NgSAI8Pn8LVf1WwvhcBg9PT0Qi8Vruii4ElNTUzh8+DB+8YtfpIVQms0iLYbSbC9Ir5PO\nzk6cOHECWVlZaG9vR0dHB/Ly8tbd1iGjJaqqqiAUCmNyRr/fTwkjv99Pzajk5OQkZduJzBkrLS2F\nRCJJ9HESAikGi4qKIJPJllX9SD8qiUSSFA7r8YKMmtmIEFKr1Thy5AjefPNN7N27N8YnTJPmqqTF\nUJrtC0EQUKvVOHbsGN577z0EAgEcOHAA7e3taxp6tdlsGBoaQkNDQ1xabwAoLxyDwQCXy0WFySZL\nGGk8xGCq4ff70d3djZKSEkil0su+TjooG41GBAKBpBe30RAKhdDT0wOpVAq5XB7VfZBC6F/+5V+w\nZ8+eGJ8wTZprkhZDadIAEWFkMBhw/PhxHD9+HEajEfv378fBgwdRX19/2Wq4Xq/H9PQ0mpqaNs35\nNhwOUzMqdrudasXk5uYmZHXd4XCgv78/rjljyQ5ZFSsvL19TyzUQCMBkMsFoNFLidr1J7ckGKYRk\nMlnUlh9pIZQmwaTFUJo0V8Jms+GDDz7AsWPHMDY2hptvvhkdHR3YtWsXfvKTn6Cnpwe/+tWvEjYP\nQhAEFSZrsVjA4XCoGZXNsBSwWq0YGRnZ1JyxZIPMm4u2KhYOh5cltccqEHgzCYVC6O7uRn5+ftTh\nw5OTk3jwwQfxy1/+Ert3747xCdOkWRNpMZQmzWp4PB589NFHeOedd/DHP/4RIpEIL7/8Mm677bak\ncJYmCAJOp5OaUWGxWJRJYDzOZzQaoVKpNrUqlmyQ7cGamhrw+fwN39/KQGA2mx3X1zAWBINB9PT0\noKCgIOqheZVKhYceegj/+q//il27dsX4hGnSrJm0GEqTZi0Eg0F8/etfB4PBwN13343jx4/j008/\nRWNjIzo6OnDbbbclTYXE7XZTA9ixTmnX6XTQarVobm7eVltSS3E6nejr64tre9DlclFzRgCoAexr\nGT1uJsFgEN3d3SgsLIxaCE1MTOChhx7Cv/3bv6GtrS3GJ4w/DAYDDQ0NIAgCDAYDb7zxBq677rpE\nHytNdKTFUJqNcfLkSTz33HMIhUJ4/PHH8eKLLy77+q9//Wu8/vrrIAgCXC4X//zP/4ympqYEnTY6\n3G43jhw5gt27d+Oll16ihl5DoRC6urrQ2dmJjz/+GCUlJbjrrrtwxx13JM0wsc/no4RRMBhc5p68\n3uHd6elpmEwmNDU1pUwbJ9bMz89jcHAQDQ0NmyZMfD4fNUTv8/kgFoshkUjA4/ESMoAdDAZx6dIl\nFBUVIS8vL6r7iIcQWu29iOTcuXPYu3cvfvvb3+LQoUNR/7ycnBw4nU4AwKlTp/CDH/wAf/zjH6O+\nvzQJJS2G0kRPKBRCZWUlfv/730Mul6OtrQ1vv/02FUMBAH/5y19QU1MDoVCIDz/8EK+88gq6uroS\neOr1Mz8/j48//hj33HPPVW9DOi+/++67+PDDDyEQCHDXXXfhrrvugkwmS4qtIXJ412AwwOPxXNE9\n+UqQOWNut/uKw+TbBZvNhuHhYTQ1NSVsRT4YDFJD9A6HAwKBABKJZNOG6EkLAYVCEbWn1tjYGB5+\n+GH8+7//e8yc9NfyXkTebv/+/cjMzMTRo0djJob++7//G7/+9a9x/PjxDT2ONAkjLYbSRM9nn32G\nV1555f9v716jmrzvOIB/o6CAioIhyqUISkG8cLGlq5cyZ/UoYoKuL+b2QilzVqlVuq2rztmj1aNl\n7YuuelZn62y1ip2SACqCCqhVW8QLggJC6wWJYAh3FAw8efaiJzmlao0hJIF8P+8wj8kvHk2+Pv//\n//dDdnY2AGDLli0AgDVr1jz2+oaGBkyYMAFqtdpqNdqCITwolUpkZGQAAGJjY6FQKBAQEGAXwejn\n3ZOHDRsGmUwGDw+PLl+qhmGjADB27Fi7qN0W6urq8P3339vVPim9Xo/GxkbU1tZ22UQ/fPjwHlnC\nNAShUaNGPbaFgCkMQWjXrl144YUXLFabqZ9FH3/8MZydnVFQUIB58+Z1KwwZlsna29tRXV2N3Nxc\ni74nsiqTPtg4tZ4eS61Wd2mu5ufn94t3fXbu3ImYmBhrlGZTEokEQUFB+Nvf/oZ33nkH1dXVSEtL\nQ1JSEhobGxETEwOFQoGxY8fa7C5L//79IZPJIJPJjF+qGo0G5eXlxlNNnp6eKC0t7bNzxkxVW1uL\nmzdvIjIy0q42M/fr1w+enp7w9PTssom+srLSON7Fy8vLIuGto6MDly9ffmIvJVOUl5dj0aJF+OKL\nLzBp0qRu1/RTpnwWqdVqqFQq5OXloaCgoNuv6erqisLCQgA/hrFFixbh6tWrDvvvxBEwDFG35eXl\nYefOnThz5oytS7EqiUQCHx8fJCYmIjExEfX19Th06BA2bdqEW7du4dVXX4VcLseLL75os2D08y/V\n5uZm3Lt3D9euXYOrqyukUik6OzsdcsN0TU0N7ty5g8jISLt+/xKJBEOGDMGQIUMwZswYtLW1oba2\nFteuXYMgCN3aK2ZoKhkYGGh2h/GeDEKmSkpKQnJyco/8O5s8ebKxf5S5YZHsH8MQPZavry/u3Llj\n/LmqquqxTdeKioqwZMkSHD161CKzwHozT09PLF68GIsXL0ZrayuysrLw2WefYcWKFZg2bRoUCgWm\nTp1qsy9eiUQCNzc3NDU1ITQ0FO7u7tBoNLh8+bJxrIRMJrObpaKedPfuXVRXVyMyMtIqvZssydXV\nFf7+/vD39zfuFTPs+3qWLuaGIDR69GhIpVKzarl+/ToWL16ML7/8EpGRkWY9x9OY8ll04cIFLFy4\nEACg1WqRmZkJJycnzJ8/v9uvX1ZWBkEQHP7zra/jniF6rM7OTgQHByMnJwe+vr6IiorCvn37MH78\neOM1lZWVmDFjBnbv3s1jp79Ap9MhNzcXKpUKZ8+eRWRkJBQKBWbMmGHVzboPHz40fvn9/C5Ae3u7\n8WSaIAjGYGQvx70t6c6dO9BqtQgLC+tTJ+cEQTA2emxqaoK7uzu8vLwwfPjwR96nTqfD5cuXMWbM\nGLODUFlZGeLj47F7925ERERY4i08limfRT8VHx9vsT1DwI976zZv3ozY2Fizn49sinuGyHxOTk7Y\ntm0bZs+eDUEQkJCQgPHjx2P79u0AgGXLluH9999HXV0dEhMTjb/nwoULtizbLg0YMABz5szBnDlz\nIAgCzp49C5VKhY0bN+L555+HXC7HnDlz4O7u3mM1PHjwAEVFRU/sqOzi4mK826DT6aDValFRUYH2\n9nabH/e2pFu3bqGpqQnh4eF97uTcT4fGiqKIpqYmYxNNFxcXYxdzURRRWFho8piRx7FWEAJM+yyy\nNEEQLP6cZN94Z4jIRvR6PQoLC6FUKpGVlQWpVAqFQoHY2FhIpVKLBY/uzBkTBMG4X6KlpQUeHh7G\nZZjeFCYMpwDb29sxbty4XlW7Jdy/fx8ajcY4FNjb2xujRo0yq5loaWkpXn/9dezZs6fX9RUjh8Sj\n9US9hSiKKC8vh1KpxKFDh+Ds7Ix58+ZBoVDAz8/P7GBkmDNmiUaCer0eDQ0N0Gg0aGxs/MVlGHti\n+LMVBAGhoaG9/u6Wudrb242bpTs6OqDRaNDR0YHhw4dDJpNhyJAhT/2zMQShr776CmFhYVaqnKhb\nGIaIeiNRFFFVVQWVSoX09HS0trYaj+yHhISY/GXek3PGDMswhmGyrq6uxmUYezqZJYoiSktL0b9/\nfwQHBzt8EPr5Mqmh0aNGo0Frays8PDzg5eX1SE8qACgpKUFCQgL27t1r3E9D1AswDBH1BVqtFunp\n6UhLS4Narcarr76KuLg4REREPHG5p7q6GlVVVVaZMyaKonEZRqvVwsnJyTiIdODAgT362r9Er9ej\npKQELi4uGDNmjMMHobFjx2LYsGFPvM5w56+2thYNDQ1obGxETU0N5s+fj+rqarz++uvYt28fgxD1\nNgxDRH1Nc3MzMjMzoVKpUFJSgujoaCgUCkyePNl4RHzr1q2YOHEiXnnlFZssX7W1tRlPpomiaDyZ\nZs1ht3q9HsXFxXB3d0dgYKDVXtfetLW14cqVK08NQj9n6E7+2WefIS8vD01NTXjjjTewfPlys2eW\nEdkIwxBRX9be3o6cnBykpqYiPz8fUVFRaG9vR21tLQ4cOGAX/YJ0Oh1qa2uh0Wig0+mMDQIHDx7c\nY3dqBEFAUVERpFJpl87FjsYQhEJDQzF06FCznuPatWtISEjAP//5T1y/fh0ZGRno6OhAbGws/vjH\nP5rdqJHIihiGiByFTqfDwoULcePGDej1eowdOxZxcXGYNWsWBg8ebOvyAPy4P8UwTPb+/fvP1CDw\nWV7jypUr8Pb2ho+Pj0WeszcytFLoThC6evUqlixZgpSUlC49fbRaLY4cOYKZM2c+thErkZ1hGCLH\nlpWVhVWrVkEQBCxZsgSrV69+7HUFBQWYPHky9u/f361GbbbS0dGB+Ph4BAYGYuPGjRBFERcvXkRq\naiqOHTsGHx8fyOVyzJ0712666Or1euMw2aamJgwdOhQymaxbE9oNw0afe+45h17KMQShcePGmd27\nqri4GH/605+wf//+R6bDE/UyDEPkuARBQHBwMI4fPw4/Pz9ERUUhJSXlkQ92QRAwa9YsuLi4ICEh\noVeGoffeew8eHh54++23H3lMFEWUlJRAqVTiyJEjcHNzMx7Z9/b2totNxaIoGofJ/nRCu1QqNXlU\nhiVmbPUF9+/fR1FRkVk9pQyKioqwdOlSBiHqKxiGyHF9++23WL9+PbKzswEAW7ZsAQCsWbOmy3Uf\nf/wxnJ2dUVBQ0O0W/rbS2dlpUmgQRRG3b9+GSqVCWloaOjo6MHfuXMjlcgQFBdlNMDJMaNdqtRgw\nYIDxZNqTpsq3t7fjypUr3eqo3BdYMgh9/fXXCA0NtXCFRDbBcRzkuNRqdZfNs35+fsjPz3/kGpVK\nhby8PBQUFFi7RIsx9e6JRCJBQEAA3n77bSQlJUGj0SA9PR2rV69GbW0tZs2ahbi4OEyYMMFmHZp/\nPqH9wYMH0Gg0uHLlCiQSifFkmmGmm2GT8JPGjDiK1tZWFBcXY+LEiWbvEbty5QreeOMN/O9//8PY\nsWMtXCGRfWMYIoeVlJSE5ORkhxvNAPwYOkaMGIGlS5di6dKlaGxsxJEjR/DRRx+hoqIC06dPh0Kh\nwEsvvWTT7tJubm4ICAhAQEAAHj58CI1Gg9LSUnR2dsLd3R11dXUYP378Mx0b72sYhIi6j8tk1CeZ\nskwWGBgIw99/rVYLNzc37NixA/Pnz7d+wXakra0Nx44dQ2pqKi5duoTJkydDLpcjOjr6iUtV1tbQ\n0IDi4mIMGjTIOFLCy8sLQ4cOtYvlPmsxzJ0LCwsze9xKYWEhli1bhgMHDiAkJMTCFRLZHPcMkePq\n7OxEcHAwcnJy4Ovri6ioKOzbt6/LEeGfio+P77V7hnpSR0cHTp06BaVSidOnTyMsLAxyuRwzZ87s\n9qwzczU1NaGkpMQYAARBMJ5Ma25uxrBhwyCTyR47UqIvsUQQunz5MpYvX46DBw8iODjYwhUS2QXu\nGSLH5eTkhG3btmH27NkQBAEJCQkYP348tm/fDgBYtmyZjSvsHZydnTFz5kzMnDkTgiAgPz8fSqUS\nycnJGDVqFORyOWJiYqy2X8cweDYiIsK4b6h///6QyWSQyWTQ6/XGk2nl5eUYMmQIvLy8IJVK7XqY\n7LNqbm5GSUkJwsPDze7sfenSJSQmJjIIEYF3hojIDHq9HlevXoVSqURmZiaGDh0KuVyOefPmYcSI\nET2yVFVXV4fvv//e5MGzoiiiubkZGo0GdXV1cHFxMZ5Ms6dhss/KEITCwsK6HYRSU1Px/PPPW7hC\nIrvCZTIi6nmiKOKHH36ASqVCRkYGAGDu3LlQKBQICAiwSDDSaDS4desWIiIizN63ZBgmW1tbi/79\n+xtPptnD2BJTNTU1obS0FOHh4cY7Y8/q4sWLePPNNxmEyFEwDBGRdYmiiJqaGmMvo4aGBsTExEAu\nlyM0NNSsPTw1NTW4c+cOIiIiLHZHp7293RiMBEEwBiNb7YMyRWNjI8rKyroVhC5cuIC33noLqamp\nCAoKsnCFRHaJYYiIbKu+vh6HDh1CWloabt68iRkzZkChUODFF180KRip1WrU1NQgPDzc5H5Kz0qn\n0xlnprW3t0MqlcLLywvu7u52czLNEIQiIiLMvpNlCEJKpRJjxoyxcIVEdothiIjsR2trK7KyspCW\nlobCwkJMnToVcXFxmDp16mPv+FRWVqKurg5hYWFW2/wsCAK0Wi1qa2vR0tICDw8P4zBZW51M++mm\ncXODUEFBAVauXGnRIPS02X979+5FcnIyRFHEkCFD8OmnnyI8PNwir030DBiGiMg+6XQ65ObmQqVS\n4ezZs4iMjIRCocCMGTPg6uqKtWvXQiaT4a233rJZCNHr9WhoaIBGo0FjYyPc3d3h5eWF4cOHWy2c\n1dfXo7y8vFtB6Pz581i1ahXS0tIQGBhokbpMmf137tw5hIaGwsPDA0ePHsX69esf6QJPZAUMQ0Rk\n/wRBwLlz56BUKnHixAm4urrCxcUFe/futZtZY6IooqmpyThM1tXV1ThMtqdOptXX16OiogIREREY\nOHCgWc+Rn5+PpKQkiwYhwPTZfwYNDQ2YMGEC1Gq1xWogMhH7DBGR/evfvz9eeeUVTJs2DUlJSVCr\n1QgJCcGCBQsglUohl8sRGxsLLy8vm+3hkUgkGDZsGIYNGwZRFI0n0y5fvgwnJyfjkX1zQ8vPGdoI\ndCcIfffdd/jzn/+M9PR0BAQEWKQuA1Nm//3Uzp07ERMTY9EaiCyJYYjIjj1tXwYAnDx5EklJSejo\n6IBUKsWpU6dsUGn3CIKAZcuWwd3dHQcOHIBEIsGmTZtQXl4OpVKJP/zhD3B2dkZsbCzi4uLg5+dn\n02A0ePBgDB48GKNHj0ZbWxs0Gg2Ki4shiqLxZJq5PYAMQSgyMtLsNgI/DUKjRo0y6zksJS8vDzt3\n7sSZM2dsWgfRL+EyGZGdMmVfRmNjI6ZMmYKsrCz4+/tDo9FAJpPZsGrzFBUVIS0tDevWrXtsyBFF\nEWq1GkqlEunp6WhtbUVMTAwUCgVCQkLs5tSXTqdDbW0tNBoNdDodpFIpZDIZBg8ebFKNWq0WN27c\n6FY/pW+//RZ/+ctfejQImbpMVlRUhAULFuDo0aPsck22wj1DRL2ZKV84//73v3H37l1s2rTJJjXa\nilarRUZGBlQqFaqqqjBz5kzExcUhIiLCbuaRdXZ2Go/s379/H56ensaTaY8LRrW1tbh582a3gtC5\nc+fw17/+FRkZGfD39+/uW3giU2b/VVZWYsaMGdi9ezemTJnSY7UQPQX3DBH1ZqbsyygvL0dHRwem\nT5+OlpYWrFq1CosWLbJ2qVYnlUqRkJCAhIQEtLS0IDMzE1u3bkVJSQmio6Mhl8sxZcqUHutNZAon\nJyeMHDkSI0eOhF6vR11dHaqrq1FWVoahQ4dCJpPB09MT/fr1M3bYjoyMNHtD9tmzZ/HOO+/0eBAC\nTJv99/7776Ourg6JiYnG33PhwoUerYvIXLwzRGSnDh48iKysLHz++ecAgD179iA/Px/btm0zXrNi\nxQpcuHABOTk5aGtrw+TJk3HkyBGHXZJ4+PAhTpw4gdTUVJw/fx5RUVFQKBSYPn26xTY3d5coisZh\nsvX19XBycoJOp8OkSZPM7ix95swZvPvuu8jIyOgSoInItDtD9nE/mcjOpaWlQSKRoKyszGqv6evr\nizt37hh/rqqqgq+vb5dr/Pz8MHv2bAwaNAhSqRTR0dG4cuWK1Wq0NwMHDkRsbCz++9//orCwEIsX\nL0Zubi6io6MRHx8PpVKJlpYWm9YokUjg4eGBkJAQBAYGorOzE15eXigqKsLly5ehVquh0+lMfj4G\nIaLu450hIhP87ne/w927dzFjxgxs2LDBKq9pyr6M0tJSrFixAtnZ2dDpdHjppZewf/9+TJgwwSo1\n9hZ6vR4XL16EUqlEdnY2fHx8MG/ePMTGxtqsl1FNTQ2qqqoQERFhXM578OCBcWaaRCIxnkx70h2j\nb775BmvWrEFGRgb8/PysWT5Rb8EN1ESW0NraipCQEOTl5UEul+P69etWe+3MzEwkJSUZ92WsXbu2\ny74MAPjwww+xa9cu9OvXD0uWLEFSUpLV6uuNRFFEaWkplEoljhw5AldXV8ybNw8KhQLe3t5WOZlW\nXV0NtVrdJQj93MOHD40n0zo7OyGVSiGRSDBq1Cj069cPp0+fxt///ncGIaJfxjBEZAl79+5Fbm4u\ndu7ciSlTpmDr1q144YUXbF0WWYAoirh9+zZUKhXS09Oh0+kwd+5cyOVyBAUF9Ugwqq6uxt27d59p\n+GxHRwe0Wi1Wr16NwsJChIeHo7i4GCdOnODSGNEvYxgisoR58+Zh1apVmDVrFj755BNUVlbio48+\nsnVZZGGiKEKj0SA9PR1paWnQaDSYNWsWFAoFJk6caJEj+3fv3kV1dTUiIiLMnm+WnZ2NLVu2IDAw\nEKWlpZg2bRoWLFiA6dOn99hoEKJejGGIqLvq6+vh5+dnHAUhCAIkEglu375tN43+qGc0NjbiyJEj\nSEtLQ3l5OaZPnw65XI5f/epXZgUZtVqNe/fuITw83OwgdOrUKaxduxaHDx+Gj48POjs7cfr0aahU\nKmi1WqSkpJj1vER9GMMQUXft2LEDFy9exH/+8x/jr/3617/Gxo0bER0dbcPKyJra2tpw7NgxKJVK\nXLx4ES+//DIUCgWio6NNapBYVVUFjUbTrSB08uRJrFu3DocOHYKPj49Zz0HkgBiGiLrrN7/5Dd59\n913MmTPH+GuffPIJSktL8emnn9qwMrKVjo4OnD59Gqmpqfjmm28wYcIEKBQKzJw5E4MGDXrk+srK\nStTV1SEsLMzsIJSXl4f33nsPhw8fhre3d3ffApEjYRgiIupJer0e+fn5UCqVOH78OEaNGgW5XI6Y\nmBh4eHjggw8+wIMHD7B+/Xqz9xzl5uZi/fr1OHToEIMQ0bNjGCIisha9Xo9r164hNTUVmZmZ0Ov1\nAIAvv/wSAQEBZu0xy8nJwYYNG3D48GGMHDnS0iUTOQJ2oCYi28vKykJISAiCgoLwwQcfPPJ4U1MT\n5HI5wsPDMX78eOzatcsGVXZfv379MHHiRKxfvx4LFy7E8OHD8dprr2HZsmWYPXs2/vWvf+HGjRsw\n9T+gJ06cYBAishLeGSKiHiMIAoKDg3H8+HH4+fkhKioKKSkpGDdunPGazZs3o6mpCcnJyaitrUVI\nSAhqamrMntxuax9++CHy8/ORkpICZ2dniKKImpoaqFQqpKWloaGhAXPmzIFCoUBoaOhjl8+OHz+O\nTZs24fDhwxgxYoQN3gVRn8E7Q0RkW+fPn0dQUBBGjx6NAQMGYOHChUhPT+9yjUQiQUtLC0RRRGtr\nKzw9PW06bb47tFotfvjhB2MQAn58f97e3khMTMSxY8eQnZ2NoKAgbN68GdOmTcM//vEPnD9/HoIg\nAGAQIrIF3hkioh5z8OBBZGVl4fPPPwcA7NmzB/n5+di2bZvxmpaWFigUCpSVlaGlpQVff/01YmNj\nbVWyVbW2tiI7OxsqlQqFhYXw9/eHWq3G8ePHIZPJbF0eUV/AO0NEZP+ys7MRERGBu3fvorCwECtW\nrEBzc7Oty7KKwYMH47XXXsNXX32FS5cuYc6cOdi7dy+DEJGVMQwRUY/x9fXFnTt3jD9XVVXB19e3\nyzW7du3Cb3/7W0gkEgQFBSEwMBBlZWXWLtXmBgwYgJUrV2LChAm2LoXI4TAMEVGPiYqKQkVFBW7e\nvAmdTof9+/dDoVB0ucbf3x85OTkAgHv37uH69esYPXq0LcolIgfVO3cpElGv4OTkhG3btmH27NkQ\nBAEJCQkYP348tm/fDgBYtmwZ1q1bh/j4eEycOBGiKCI5ORlSqdTGlRORI+EGaiKiPiIrKwurVq2C\nIAhYsmQJVq9e3eVxURSxatUqZGZmws3NDV988QUmTZpko2qJrIIbqImIHIUgCHjzzTdx9OhRlJSU\nICUlBSUlJV2uOXr0KCoqKlBRUYEdO3Zg+fLlNqqWyL4wDBER9QGm9HRKT0/HokWLIJFI8PLLL6Ox\nsRHV1dU2qpjIfjAMERH1AWq1Gs8995zxZz8/P6jV6me+hsgRMQwRERGRQ2MYIiLqA0zp6WTKNUSO\niGGIiKgPMKWnk0KhwO7duyGKIr777jsMHToU3t7eNqqYyH6wzxARUR9gSk+nuXPnIjMzE0FBQXBz\nc8OuXbtsXDWRfWCfISIiIuqr2GeIiMgSEhISIJPJnjg3TBRFrFy5EkFBQQgLC8OlS5esXCERdQfD\nEBHRU8THxyMrK+uJj7OZIVHvxjBERPQU0dHR8PT0fOLjbGZI1LsxDBERdRObGRL1bgxDRERE5NAY\nhoiIuonNDIl6N4YhIqJuYjNDot6NTReJiJ7i97//PU6ePAmtVgs/Pz9s2LABHR0dANjMkKgvYNNF\nIiIi6qvYdJGIiIjoaRiGiIiIyKExDBEREZFDYxgiIiIih8YwRERERA6NYeGCSd8AAACESURBVIiI\niIgcGsMQEREROTSGISIiInJoDENERETk0BiGiIiIyKExDBEREZFDe9ZBrSbN+CAiIiLqLXhniIiI\niBwawxARERE5NIYhIiIicmgMQ0REROTQGIaIiIjIoTEMERERkUNjGCIiIiKHxjBEREREDo1hiIiI\niBwawxARERE5tP8DJgtjIfwuE7EAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11bcf18d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from mpl_toolkits.mplot3d.axes3d import Axes3D\n",
    "\n",
    "def map2(fn, A, B):\n",
    "    \"Map fn to corresponding elements of 2D arrays A and B.\"\n",
    "    return [list(map(fn, Arow, Brow))\n",
    "            for (Arow, Brow) in zip(A, B)]\n",
    "\n",
    "cutoffs = arange(0.00, 1.00, 0.02)\n",
    "A, B = np.meshgrid(cutoffs, cutoffs)\n",
    "\n",
    "fig = plt.figure(figsize=(10,10))\n",
    "ax = fig.add_subplot(1, 1, 1, projection='3d')\n",
    "ax.set_xlabel('A')\n",
    "ax.set_ylabel('B')\n",
    "ax.set_zlabel('Pwin(A, B)')\n",
    "ax.plot_surface(A, B, map2(Pwin, A, B));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What does this [Pringle of Probability](http://fivethirtyeight.com/features/should-you-shoot-free-throws-underhand/) show us? The highest win percentage for **A**, the peak of the surface, occurs when *A* is around 0.5 and *B* is 0 or 1. We can confirm that, finding the maximum `Pwin(A, B)` for many different cutoff values of `A` and `B`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "cutoffs = (set(arange(0.00,    1.00,    0.01)) | \n",
    "           set(arange(0.500,   0.700,   0.001)) | \n",
    "           set(arange(0.61803, 0.61804, 0.000001)))\n",
    "\n",
    "def Pwin_summary(A, B): return [Pwin(A, B), 'A:', A, 'B:', B]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.625, 'A:', 0.5, 'B:', 0.0]"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(Pwin_summary(A, B) for A in cutoffs for B in cutoffs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So **A** could win 62.5% of the time if only **B** would chose a cutoff of 0. But, unfortunately for **A**, a rational player **B** is not going to do that. We can ask what happens if the game is changed so that player **A** has to declare a cutoff first, and then player **B** gets to respond with a cutoff, with full knowledge of **A**'s choice. In other words, what cutoff should **A** choose to maximize `Pwin(A, B)`, given that **B** is going to take that knowledge and pick a cutoff that minimizes `Pwin(A, B)`? "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.5, 'A:', 0.61803400000000008, 'B:', 0.61803400000000008]"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max(min(Pwin_summary(A, B) for B in cutoffs)\n",
    "    for A in cutoffs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And what if we run it the other way around, where **B** chooses a cutoff first, and then **A** responds?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.5, 'A:', 0.61803400000000008, 'B:', 0.61803400000000008]"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min(max(Pwin_summary(A, B) for A in cutoffs)\n",
    "    for B in cutoffs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In both cases, the rational choice for both players in a cutoff of 0.618034, which corresponds to the  \"saddle point\" in the middle of the plot. This is a *stable equilibrium*; consider fixing *B* = 0.618034, and notice that if *A* changes to any other value, we slip off the saddle to the right or left, resulting in a worse win probability for **A**. Similarly, if we fix *A* = 0.618034, then if *B* changes to another value, we ride up the saddle to a higher win percentage for **A**, which is worse for **B**. So neither player will want to move from the saddle point.\n",
    "\n",
    "The moral for continuous spaces is the same as for discrete spaces: be careful about defining your sample space; measure carefully, and let your code take care of the rest."
   ]
  }
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